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López, Antonio Fernández and García, Esther and Lozano, Miguel Gómez
An Artinian theory for Lie algebras
DOI: 10.1016/j.jalgebra.2007.10.038
Description: A Lie algebars is called complemented if for any inner ideal N there is an inner ideal M such that L = M + {x\in L | [N,[N,x]] = 0} = N + {x\in L | [M,[M,x]] = 0}.
La Scala, Roberto
An algorithm for complexes
ISAAC 94, 264-268
Description: Given a finite complex of modules over a polynomial ring, an algorithm is presented which transforms it in a resolution of Grobner type.
Availability: complexes.djvu
Labra, Alicia and Suazo, Avelino
On plenary train algebras of rank 4
DOI: 10.1080/00927870701353589
Comm. Algebra 35 (2007), N9, 2744-2752
Availability: 782314245_content.pdf
Labute, John P.
Algebres de Lie et pro-p-groupes definis par une seule relation
Inv. Math. 4 (1967), 142-158
Availability: hardcopy
Ladoshkin, M.V.
A_\infty-modules over A_\infty algebras and the Hochschild cohomology complex for modules over algebras
Mat. Zametki 79 (2006), N5, 717-728
(me)
Availability: hardcopy
Laffey, Thomas J.
On commutative subrings of infinite rings
DOI: 10.1112/blms/4.1.3
Bull. Lond. Math. Soc. 4 (1972), 3-5
Zentralblatt: 0242.16029
Description: An infinite associative ring contains an infinite commutative subring.
Availability: 3.pdf
Finite groups with a unique minimal normal subgroup
J. London Math. Soc. 5 (1972), 222
MR 46#9152
Zentralblatt: 0238.20028
Commutative subalgebras of infinite dimensional algebras
DOI: 10.1112/blms/5.3.312
Bull. London Math. Soc. 5 (1973), N3, 312-314
MR 48#6185
Zentralblatt: 0267.16016
Description: Any infinite associative ring contains an infinite commutative subring and an infinite-dimensional algebra over a field contains an infinite-dimensional commutative subalgebra.
Infinite rings with all proper subrings finite
Amer. Math. Monthly 81 (1974), 270-272
MR 49#2710
Zentralblatt: 0277.16013
Commutative subrings of periodic rings
Math. Scand. 39 (1976), no.2, 161-166
MR 55#8016
Zentralblatt: 0344.16023
Description: Infinite associative rings all whose subsets x, x^2, x^3 ,... are finite for any element x.
Square zero subalgebras of algebras
Proc. Roy. Irish Acad. Sect. A 76 (1976), no.27, 301-303
MR 55#8078
Zentralblatt: 0344.16006
Description: When an infinite-dimensional associative algebra contains an infinite-dimensional square-zero subalgebra?
On the structure of algebraic algebras
Pacific J. Math. 62 (1976), no.2, 461-471
MR 53#13304
Zentralblatt: 0313.16022
Description: Any infinite-dimensional associative algebra has an infinite-dimensioanl commutative subalgebra of one of the specific types.
Simultaneous triangularization of a pair of matrices
DOI: 10.1016/0021-8693(77)90200-9
J. Alg. 44 (1977), 550-557
Description: Criterion for sumiltaneous triangularization.
Availability: sdarticle-1.pdf
Commutative R-subalgebras of R-infinite R-algebras and the Schmidt problem for R-algebras
Studies in algebra and number theory, Adv. in Math. Suppl. Stud., 6, Academic Press, New York-London, 1979, 357-369
MR 80j:17013
Zentralblatt: 0461.16018
Description: Any R-infinite alternative algebra over a commutative associative ring R with identity always contains an R-infinite commutative associative subalgebra. Study of R-infinite alternative algebras all of whose proper subalgebras are R-finite.
The minimal dimension of maximal commutative subalgebras of full matrix algebras
DOI: 10.1016/0024-3795(85)90247-2
Linear Algebra Appl. 71 (1985), 199-212
Zentralblatt: 0578.15008
Conjugacy and factorization results on matrix groups
Functional analysis and operator theory (ed. J.Zemanek), Banach Cent. Publ. 30 (1994), 203-221
Description: Multiplicative and additive commutators.
Availability: hardcopy
Laffey, Thomas J. and Reams, Robert
Integral similarity and commutators of integral matrices
Linear Algebra Appl. 197-198 (1994), 671-689
Zentralblatt: 0801.15015
Description: Shoda's result that every element of trace zero in M_n(K) is a commutator is extended for matrices over integers.
Laffey, T.J. and West, T.T.
Trace-zero matrices and polynomial commutators
Ir. Math. Soc. Bull. 31 (1993), 11-13
Zentralblatt: 0804.15009
Description: Furhther musing on the theme of representability of trace zero matrix by commutators.
Lagarias, Jeffrey C.
The 3x+1 problem and its generalizations
Amer. Math. Monthly 92(1985), No.1, 3-23
Availability: 0-150.pdf; hardcopy
The 3x+1 problem: An annotated bibliography
Description: This one is periodically updated, so check the latest version on arXiv.
Availability: hardcopy (version of Nov 10, 2004, not the latest!)
The 3x+1 Problem: An Annotated Bibliography, II (2001-)
math.NT/0608208, 20 pages
Lagarias, J.C. and Weiss, A.
The 3x+1 problem: two stochastic models
Ann. Appl. Probab. 2(1992), 229-261
Availability: 2nd.pdf
Laglasse-Decauwert, Monique
Sur les sous-algèbres reductives d'une algèbre de Lie
C. R. Acad. Sci., Paris, Sér. A 277, 969-971 (1973)
Zentralblatt: 0269.17003
Description: Almost algebraic Lie algebras.
Lagno, V.I. and Spichak, S.V. and Stognii, V.I.
Simmetriinyi analiz uravnenii evolyucionnogo tipa
Inst. Comput. Issled., Moscow-Izhevsk, 2004 (in Russian)
Availability: Kolkhoz
Laita, Luis M. and Ledesma, Luis de and Roanes-Lozano, Eugenio
An interpretation of the propositional Boolean algebra as a k-algebra. Effective calculus
DOI: 10.1007/3-540-60156-2_18
Lect. Notes Comp. Sci. 958 (1995), Integrating Symbolic Mathematical Computation and Artificial Intelligence, 255-263
Availability: 1995-interpretation.pdf
Laita, L. M. and Roanes-Lozano, E. and Ledesma, L. de and Alonso, J. A.
DOI: 10.1007/s005000050086
A computer algebra approach to verification and deduction in many-valued knowledge systems
Soft Computing 3 (1999), N1, 7-19
Description: A predicate formula A (in many-valued logic) is a consequence of formulae A_0, ...., A_1, iff the polynom of negation of A lies in an ideal generated by polynoms of negations of A_0, ..., A_1.
Availability: 1999-computer.pdf
Laita, L. M. and Roanes-Lozano, E. and Maojo, V.
Inference and verification in medical appropriateness criteria using Gröbner bases
DOI: 10.1007/BFb0055897
Lect. Notes Comp. Sci. 1476 (1998), Artificial Intelligence and Symbolic Computation
Description: Previous author's approach of reducing a question about concequence of formulas in many-valued logic to ideal membership problem in polynomial ring, is applied to a knowldge base of a concrete medical problem.
Availability: 1998-inference.pdf
Laliena, Jesus and Sacritan, Sara
Lie structure in semiprime superalgebrs with superinvolution
math.RA/0701357
Lallement, Gerard
Semigroups and Combinatorial Applications
Mir, 1985 (Russian translation from Wiley, 1979)
Availability: Kolkhoz (Russian edition); 1979-semigroups.djvu
Lalonde, Pierre and Ram, Arun
Standard Lyndon bases of Lie algebras and enveloping algebras
Trans. Amer. Math. Soc. 347 (1995), no. 5, 1821--1830
MR 95h:17013
Zentralblatt: 0833.17003
MR Review: The authors extend the method of obtaining a basis for the free associative algebra over an alphabet $A$ by multiplying ordered sequences of standard Lie bracketings of Lyndon words over $A$ to the general case of the enveloping algebra of an arbitrary Lie algebra. If the latter is given as a factor algebra of the free Lie algebra over $A$, the set of all Lyndon words over $A$ has to be replaced by a certain rather natural subset for this purpose. Finally, this subset is calculated for presentations of the complex finite-dimensional simple Lie algebras.
Lam, Ngau
Extensions of modules over supercurrent conformal algebras
Comm. Alg. 29 (2001), N7, 3061-3068
Availability: 100105006.pdf
Lam, T.Y.
Lectures on Modules and Rings
Springer, 1999
Description: Frobenius and quasi-frobenius rings (especially p. 442 onwards) p. 453: terminology: why Frobenius and not Frobeniusean.
Availability: Kolkhoz; 1999-lectures.djvu; google books
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Exercises in Classical Ring Theory
Springer, 2003
Availability: Kolkhoz
LaMacchia, B. A. and Odlyzko, A. M.
Solving Large Sparse Linear Systems Over Finite Fields
Lambe, L. A. and Seiler, W. M.
Differential equations, Spencer cohomology, and computing resolutions
Georgian Math. J. 9 (2002), 723-774
Abstract: We propose a new point of view of the Spencer cohomology appearing in the formal theory of differential equations based on a dual approach via comodules. It allows us to relate the Spencer cohomology with standard constructions in homological algebra and, in particular, to express it as a Cotor. We discuss concrete methods for its construction based on homological perturbation theory.
Availability: llws.pdf
Lambe, Larry and Stasheff, Jim
Applications of perturbation theory to iterated fibrations
Manuscr. Math. 58(1987), N3, 363 - 376
Description: Gugenheim's homological perturbation theory.
Availability: h76w6815228101up.pdf
Lambek, Joachim
Lectures on Rings amd Modules
Mir, 1971 (Russian translation from Blaisdell, 1966)
Availability: 1966-lectures.djvu
Lamy, S.
L'alternative de Tits pour Aut[C^2]
J.Alg. 239(2001), 413-437
Lancaster, P.
Matrix Theory
Nauka, Moscow, 1973 (in Russian)
Availability: Kolkhoz; absent on amazon
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Lancaster, P. and Rodman, L.
Algebraic Riccati Equations
Clarendon Press, Oxford, 1995.
Lanczos, C.
Applied Analysis
Gos. Izdat. Fiz.-Mat. Lit, 1966 (Russian translation from Prentice Hall, 1956)
Description: Including Lanczos method and around.
Availability: 1956-applied.djvu
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Landers, D. and Rogge, L.
Characterization of the topologies used in the theory of maximum likelihood estimation
DOI: 10.1007/BF00538392
Probability Theory and Related Fields Volume 21, Number 3 / September, 1972 Pages 197-200
Availability: 1972-characterization.pdf
Landi, G. and Marmo, G. and Vilasi, G.
An algebraic approach to integrability
ESI Preprint, 2 (1993)
Description: Agreeable Poisson structures.
Availability: esi002.ps
Lando, S.K.
Lekcii o proizvodyashchikh funkciyakh
MCCME, 2004 (in Russian)
Availability: Kolkhoz
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Landsberg, Joseph M. and Manivel, Laurent
The projective geometry of Freudenthal's magic square
J. Algebra 239 (2001), 477-512
arXiv:math/9908039
Construction and classification of complex simple Lie algebras via projective geometry
DOI: 10.1007/s00029-002-8103-5
Selecta Math. 8 (2002), N1, 137-159
arXiv:math/9902102 (under different tittle)
Description: Classification via elementary algebraic geometry, not using root systems.
Triality, exceptional Lie algebras and Deligne dimension formulas
DOI: 10.1006/aima.2002.2071
Adv. Math. 171 (2002), N1, 59-85
arXiv:math/0107032
The sextonions and E_{7\frac 12}
DOI: 10.1016/j.aim.2005.02.001
Adv. Math. 201 (2006), N1, 143-179
arXiv:math.RT/0402157
Abstract: We fill in the "hole" in the exceptional series of Lie algebras that was observed by Cvitanovic, Deligne, Cohen and deMan. More precisely, we show that the intermediate Lie algebra between $E_7$ and $E_8$ satisfies some of the decomposition and dimension formulas of the exceptional simple Lie algebras. A key role is played by the sextonions, a six dimensional algebra between the quaternions and octonions. Using the sextonions, we show similar results hold for the rows of an expanded Freudenthal magic chart. We also obtain new interpretations of the adjoint variety of the exceptional group $G_2$.
Landsberg, J.M. and Robles, C.
Fubini-Griffiths-Harris rigidity and Lie algebra cohomology
arXiv:0707.3410
Description: Cartan prolongations.
Landsman, N. P.
Quantization as a functor
Contemporary Mathematics 315 (2002)
Landweber, Gregory D.
Twisted representation rings and Dirac induction
math.RT/0403524
Description: Representation rings of Lie superalgebras.
K-theory and elliptic operators
math.AT/0504555
Description: Introduction to the Atiyah-Singer index theorem.
Representation rings of Lie superalgebras
math.RT/0403203
K-Theory Volume 36, Numbers 1-2 2005 Pages: 115 - 168
Abstract: Given a Lie superalgebra $\g$, we introduce several variants of the representation ring, built as subrings and quotients of the ring $R_{\Z_{2}}(\g)$ of virtual $\g$-supermodules (up to even isomorphisms). In particular, we consider the ideal $R_{+}(\g)$ of virtual $\g$-supermodules isomorphic to their own parity reversals, as well as an equivariant $K$-theoretic super representation ring $SR(\g)$ on which the parity reversal operator takes the class of a virtual $\g$-supermodule to its negative. We also construct representation groups built from ungraded $\g$-modules, as well as degree-shifted representation groups using Clifford modules. The full super representation ring $SR^{*}(\g)$, including all degree shifts, is then a $\Z_{2}$-graded ring in the complex case and a $\Z_{8}$-graded ring in the real case. Our primary result is a six-term periodic exact sequence relating the rings $R^{*}_{\Z_{2}}(\g)$, $R^{*}_{+}(\g)$, and $SR^{*}(\g)$. We first establish a version of it working over an arbitrary (not necessarily algebraically closed) field of characteristic 0. In the complex case, this six-term periodic long exact sequence splits into two three-term sequences, which gives us additional insight into the structure of the complex super representation ring $SR_{\C}^{*}(\g)$. In the real case, we obtain the expected 24-term version, as well as a surprising six-term version of this periodic exact sequence.
Lang, S.
SL2(R)
Addison-Wesley, 1975; hardcover, 428 pp.
Availability: hardcopy (book); Kolkhoz
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Algebra
URL: http://www.krelib.com/matematika/1073 http://www.vargin.mephi.ru/booksAlgebra.html http://techlibrary.ru/books.htm http://da8.boom.ru/ct/algebra.htm http://lib.prometey.org/?id=14853&page=3
revised 3rd ed., Springer, 2002; hardcover, 914 pp.
Availability: hardcopy (book); Kolkhoz
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Lange, K.
Numerical Analysis for Statisticians
Springer, 1999
Availability: num-analysis.pdf
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Mathematical and Statistical Methods for Genetic Analysis
2nd ed., Springer, 2006; hardcover
Availability: hardcopy (book)
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Langer, Helmut
An interesting application of algebra to genetics
Elem. Math. 60 (2005), no. 1, 25--32
Description: Problem of associating phenotypes to genotypes is formulated in terms of semilattices.
Availability: 2005-60-01-04.pdf; hardcopy
Lanski, Charles
Lie ideals and derivations in rings with involution
Pacific J. Math. 69 (1977), N2, 449-460
MR 0485976
Zentralblatt: 0345.16015|0333.16012
Lanski, C. and Montgomery, S.
Lie structure of prime rings of characterists 2
Pacific J. Math. 42(1972), 117-136
Lapin, S.V.
D_\infty-differentials and A_\infty structures in spectral sequences (in Russian)
Sovrem. Matem. i ee Prilozh. 1 (2003), 56-91
(me)
Description: Homological perturbation theory.
Availability: hardcopy
Laplace, Pierre Simon
A Philosophical Essay on Probabilities
Dover, 1951
Availability: hardcopy
Larsen, Michael and Lindenstrauss, Ayelet
Topological Hochschild homology and the condition of Hochschild-Kostant-Rosenberg
Comm. Alg. 29(2001), N4, 1627-1638
Availability: 100002122.pdf
Larson, Loren C.
A Theorem about Primes Proved on a Chessboard
Mathematics Magazine, Vol. 50, No. 2 (Mar., 1977), pp. 69-74
Availability: 0.pdf
Larsson, Daniel and Silvestrov, Sergei D.
Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities
DOI: 10.1016/j.jalgebra.2005.02.032
J. Algebra 288 (2005), N2, 321-344
arXiv:math.RA/0408061
Description: Generalization of color Lie algebras; q-deformations of Witt and Virasoro. Quasi-hom-Lie deformations of loop algebras and their "central extensions".
Quasi-Lie algebras
Noncommutative Geometry and Representation Theory in Mathematical Physics (ed. J.Fuchs et al.), Contemp. Math. 391 (2005), 241--248
The Lie algebra sl_2(F) and quasi-deformations
Czechoslovak J. Phys. 55 (2005), no. 11, 1467--1472
Graded quasi-Lie algebras
Czechoslovak J. Phys. 55 (2005), no. 11, 1473--1478
Quasi-deformations of sl_2(F) with base R[t,t^{-1}]
DOI: 10.1007/s10582-006-0429-3
Czechoslovak J. Phys. 56 (2006), no. 10-11, 1227--1230
Quasi-deformations of sl_2(F) using twisted derivations
DOI: 10.1080/00927870701545127
Comm. Algebra 35 (2007), N12, 4303-4318
arXiv:math.RA/0506172
Description: Some deformations of sl(2) in non-classical sense (in broader categories?).
Larsson, Anna
A periodisation of semisimple Lie algebras
URL: http://www.math.su.se/reports/2001/15/ http://www.intlpress.com/hha/v4/n2/a15/
HHA 4 (2002), 337-355
Zentralblatt: 0995.17009 (me)
Description: (among all) reasonings and facts about root space decompositions and root systems in simple Lie algs (over C).
Availability: hardcopy
Larsson, T.A.
Extensions of diffeomorphism and current algebras
arXiv:math-ph/0002016
Description: Dzhumadil'daev has classified all tensor module extensions of $diff(N)$, the diffeomorphism algebra in $N$ dimensions, and its subalgebras of divergence free, Hamiltonian, and contact vector fields. I review his results using explicit tensor notation. All of his generic cocycles are limits of trivial cocycles, and many arise from the Mickelsson-Faddeev algebra for $gl(N)$. Then his results are extended to some non-tensor modules, including the higher-dimensional Virasoro algebras found by Eswara Rao/Moody and myself. Extensions of current algebras with $d$-dimensional representations are obtained by restriction from $diff(N+d)$. This gives a connection between higher-dimensional Virasoro and Kac-Moody cocycles, and between Mickelsson-Faddeev cocycles for diffeomorphism and current algebras.
Availability: hardcopy
Structure preserved by consistently graded Lie superalgebras
arXiv:math-ph/0106004
Description: Musings on the theme of Cartan prolongations.
Lascoux, Alain
Syzygies des varie'te's de'terminantales
Adv. Math. 30(1978), N3, 202-237
Description: Schur functors, (generalized) Cauchy formulas in characteristic 0 (seems to characteristic 0 precessor of Akin-Buchsbaum-Weyman).
Availability: sdarticle.pdf
Symmetric Functions and Combinatorial Operators on Polynomials
AMS, 2003
Availability: 44$
The differential equation satisfied by a plane curve of degree n
Bulletin des Sciences Mathe'matiques Volume 130, Issue 4, 2006, Pages 354-359
Description: Amazing manipulations with derivatives.
Availability: 2006-diffeq.pdf
Lashi, Alexander A. (=Lashkhi)
Proektirovanie Magnusovykh kolec i algebr Lie
Trudy Gruzinsk. Politechn. Inst. 1971, N8, 7-11
Izolirovannye podalgebry pri strukturnykh izomorphizmakh algebr Lie
Trudy Gruzinsk. Politechn. Inst. 1973, N6, 133-135
Strukturnye izomorfizmy nekotorykh klassov algebr Lie
Trudy Tbilis. Mat. Inst. AN GruzSSR 46(1975), 5-21
Strukturnye izomorfizmy kolec i algebr Lie
Doklady AN SSSR 228 (1976), N3, 537-539
Projection of wreath products of Lie algebras
Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 69 (1980), no.6, 313--316
MR 84e:17006
Description: Projection is isomorphism of subalgebras of lattices.
Lattices with modular identity and Lie algebras
DOI: 10.1007/BF01088205
J. Math. Sci. 38 (1987), N2, 1823-1853
VINITI, Vol. 26, 1984, 213-
On Lie algebras with modular lattices of subalgebras
J. Algebra 99 (1986), no. 1, 80-88
MR 87h:17027
Lattices of subalgebras of solvable Lie algebras
Contemp. Math. 131, Part 2 (1992), 69--89
MR 93j:17012
Availability: hardcopy (book)
A projective geometry of Lie algebras
DOI: 10.1134/S1064562407060154
Doklady Mathematics Volume 76, Number 3 / December, 2007 Pages 866-868
Description: Lattice isomorphisms of Lie algebras.
Lashkhi, Alexander A. and Zimmermann, Irene
On Lie algebras with many nilpotent subalgebras
DOI: 10.1080/00927870500387796
Comm. Algebra 34(2006), N2, 595 - 600
Description: Over commutative domain.
Laszkiewicz, Beata and Zietak, Krystyna
Approximation by matrices with restricted spectra
DOI: 10.1016/j.laa.2007.09.009
Lin. Alg. Appl. Volume 428, Issue 4, 1 February 2008, Pages 1031-1040
Description: Related to "coposede".
Lass, Bodo
On the combinatorics of the graph-complex
CRAS 334 (2002), 1-6
Zentralblatt: (me)
Availability: hardcopy
Latyshev, V.N.
K teoreme Regeva o tojdestvah tenzornogo proizvedeniya PI-algebr
UMN 27 (1972), N4, 213-214 (exists in Russian only)
Availability: hardcopy
Kombinatornaya teoriya kolec. Standartnye basisy
Moscow Univ., 1988 (in Russian)
Availability: Kolkhoz
Latyshev, V.N. and Mikhalev, A.V. and Pikhtilkov, S.A.
On the sum of locally solvable ideals of Lie algebras
Vestnik MGU 2003, N3, 29-32
Description: Example of a Lie algebra in which sum of a two locally solvable ideal isn't locally solvable (answering a question from Amayo-Stewart book).
Lau, Michael Kekainalu
Fock representations and central extensions
PhD Thesis, The Univ. of Wisonsin-Madison, 2004, 98 pages
Description: Including central extensions of gl_n over Weyl algebra. Seems to be particular cases of earlier more general results.
Bosonic and fermionic representations of Lie algebra central extensions
DOI: 10.1016/j.aim.2004.06.005
Adv. Math. 194 (2005), N2, 225-245
arXiv:math.RT/0405576
MR 2005m:17008
On universal central extensions of sl_n(A)
Infinite-dimensional aspects of representation theory and applications, Contemp. Math. 392 (2005), 43--54
MR 2006m:17019 (me)
Availability: hardcopy
Laubenbacher, Reinhard and Stigler, Brandilyn
A computational algebra approach to the reverse engineering of gene regulatory networks
DOI: 10.1016/j.jtbi.2004.04.037
arXiv:q-bio/0312026
Journal of Theoretical Biology 229 (2004) 523-537
Description: Reduce system of boolean equations to a system of polynomial equations over GF(2).
Availability: hardcopy
Laudal, O. A.
Noncommutative deformations of modules
Homology, Homotopy and Applications, Vol. 4(2), 2002, pp. 357-396
Abstract: The classical deformation theory for modules on a k-algebra, where k is a field, is generalized. For any k-algebra, and for any finite family of r modules, we consider a deformation functor defined on the category of Artinian r-pointed (not necessarily commutative) k-algebras, and prove that it has a prorepresenting hull, which can be computed using Massey-type products in the Ext-groups. This is first used to construct k-algebras with a preassigned set of simple modules, and to study the moduli space of iterated extensions of modules. In forthcoming papers we shall show that this noncommutative deformation theory is a useful tool in the study of k-algebras, and in establishing a noncommutative algebraic geometry.
Launois, Stephane and Richard, Lionel
Twisted Poisson duality for some quadratic Poisson algebras
arXiv:math.KT/0609390
Description: Poisson cohomology of Poisson algebras.
Poisson (co)homology of truncated polynomial algebras in two variables
arXiv:0805.4694
Lauret, Jorge
Degenerations of Lie algebras and geometry of Lie groups
DOI: 10.1016/S0926-2245(02)00146-8
Diff. Geom. Appl. 18 (2003), N2, 177-194
Rational forms of nilpotent Lie algebras and Anosov diffeomorphisms
DOI: 10.1007/s00605-008-0562-0
Monatshefte für Mathematik Volume 155, Number 1 / September, 2008 Pages 15-30
Description: All rational forms of nilpotent Lie algebras up to dimension 8.
Lavrov, I.A. and Maksimova, L.L.
Zadachi po teorii mnozhestv, matematicheskoi logike i teorii algoritmov
4th ed., Fizmatlit, Moscow; paperback, 256 pp. (in Russian)
Availability: hardcopy (book); Kolkhoz (5th ed.)
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Lawrence, John
When is the tensor product of algebras local? II
PAMS >= 1975
The definability of the commutator subgroup in a variety generated by a finite group
Canad. Math. Bull. 28 (1985), no. 4, 505--507
MR Review: The commutator subgroup is said to be definable in a variety $V$ of groups if there exists a first-order formula $\varphi(x)$ such that, for every group $H$ in $V$, the commutator subgroup $H'$ is the set of those $a$ in $H$ satisfying $\varphi(a)$. Theorem 2: If $V$ contains a finite nonabelian group, then the commutator subgroup is not definable in $V$. It is an open question whether every variety that contains some nonabelian group must contain a finite nonabelian group. The key to the proof is Theorem 1: If a class $C$ of groups is closed under ultraproducts, then the commutator subgroup is definable in $C$ if and only if, for some positive integer $k$, every product of commutators in a group $H$ in $C$ is a product of $k$ commutators.
The Jacobson radical of tensor products
Q. J. Math. 42 (1991), 203-208
Zentralblatt: 0726.16014
Laytimi, F. and Nahm, W.
Vanishing theorems for products of exterior and symmetric powers
math.AG/9809064
Description: cohomology groups H^{p,q}(X, S_I(E)) for a complex variety X and Schur functor S_I.
Laywine, Charles F. and Mullen, Gary L.
Discrete Mathematics Using Latin Squares
Wiley, 1998
Availability: Kolkhoz
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Lazard, D.
CRAS 234(1952)
Description: Any Lie ring can be embedded in R^(-) for some associative ring R.
DOI: 10.1007/3-540-12868-9_99
Gro"bner bases, Gaussian elimination and resolution of systems of algebraic equations
Lecture Notes in Computer Science Volume 162/1983 Pages 146-156
Availability: 1983-groebner.pdf
Lazerson, E.
Onto inner derivations in division rings
BAMS 67(1961), 356-368
Zentralblatt: 0104.03302
Description: Example of an (infinite-dimensional) division ring D such that [x,D] = D for some element x over p>0.
Le Bruyn, Lieven
alg@n
Description: Part of the book; chapter 4 contains (among other) interesting (known) reasonings about Young diagrams and morphisms of algebraic varieties.
Le'andre, R.
Anticipative Chen-Souriau cohomology and Hochschild cohomology
Confe'rence Moshe' Flato 1999 Quantization, Deformations, and Symmetries Volume II
Kluwer, 2000
Lebedev, Alexei and Leites, Dmitry
A realization of the Steenrod algebra
J. Prime Research Math. 2(2006), N1, 1-13
Availability: Steen1.pdf; hardcopy (6 p. previous version)
Determinant Shapovalova dlya superalgebr petel
Manuscript
Availability: CasimRUS1.pdf
Lebedev, Alexei and Leites, Dmitry and Shereshevskii, Ilya
Lie superalgebra structures on C^*(n,n) and H^*(n,n)
Lie Groups and Invariant Theory (ed. E.Vinberg), AMS, 2005, 157-172
arXiv:math.KT/0404139
Zentralblatt: (me)
Availability: hardcopy
Lebedev, D.R. and Manin, Yu.I.
Gelfand-Dikii Hamiltonian operator and the coadjoint of the Volterra group
Funct. Anal. Apppl. 13 (1979), 268-
Selected Papers of Yu.I. Manin, World Sci., 1996,
Description: Virasoro-like looking Lie algebra in two variables, dubbed "Lie-Volterra algebra".
Availability: 1996-selecta.djvu (whole book)
Lebedev, Aleksei
Invariants of nonholonomic systems and cohomology superalgebras of nilpotent Lie algebras
M.Sc. Thesis, Nijnii Novgorod Univ., 2003
Availability: diplom3.pdf; hardcopy
Nondegenerate bilinear forms in characteristic 2, related contact forms, simple Lie algebas and superalgebras
arXiv:math.AC/0601536
Availability: hardcopy
On the Bott-Borel-Weil theorem
DOI: 10.1134/S0001434607030169
Math. Notes 81 (2007), N3-4, 417-421
Zentralblatt: (me)
Description: Cohomology of the nilradical of Borel subalgebra with trivial coefficients as a commutative superalgebra.
Availability: hardcopy (Russian and English)
Simple modular Lie superalgebras
PhD Thesis
Availability: ALmis91.pdf
Lebedev, N.N.
Special Functions and Applications
Dover, 1972; paperback, 308 pp.
Availability: hardcopy (book); Kolkhoz (Russian); Kolkhoz' obmennik (English)
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Leborgne, Daniel
Cohomologie des aneaux de Lie et obstructions
CRAS 264(1967), 231-234
Description: the same 3-dim. cohomology and obstructions and kernels theme
Lecomte, P. B. A.
Application of the cohomology of graded Lie algebras to formal deformations of Lie algebras
Lett. Math. Phys. 13 (1987), no. 2, 157-166
Lecomte, P. B. A. and Melotte, D. and Roger, C.
Explicit form and convergence of 1-differential formal deformations of the Poisson Lie algebra
Lett. Math. Phys. 18 (1989), no. 4, 275--285
Lecomte, P.A.B. and Michor, P.W. and Schiketanz, H.
The multigraded Nijenhuis-Richardson algebra, its universal property and applications
JPAA 77(1992), N1, 87-102
math.QA/9201257
Availability: hardcopy
Lecomte, P.B.A. and Ovsienko, V.Yu.
Cohomology of the vector fields Lie algebra and modules of differential operators on a smooth manifold
URL: http://www.ingentaconnect.com/content/klu/comp/2000/00000124/00000001/00248137 http://www.springerlink.com/content/gx1m4661t24500q7/
DOI: 10.1023/A:1002447724679
Compos. Math. 124 (2000), No.1, 95-110
arXiv:math.DG/9905058
Zentralblatt: 0968.17007
Description: H^1; modules of "tensor densities" F_\lambda are involved.
Lecomte, P.A.B. and Roger, C.
Sur les de'formations des alge`bres de courants de type re'ductif
C. R. Acad. Sci. Paris Se'r. I Math. 303 (1986), no. 16, 807--810.
Availability: hardcopy
Rigidity of current Lie algebras of complex simple Lie type
J. London Math. Soc. 37(1988), no.2, 232-240.
Availability: hardcopy
Modules et cohomologie des bigebres de Lie
CRAS 310(1990), 405-410; Erratum: 311(1990), no. 13, 893-894
Description: More conceptual approach to the Nijenhuis-Richardson superalgebra structure on H^*(L,L) ?
Availability: hardcopy
Remarques sur la cohomologie de l'alge`bre de Nijenhuis-Richardson
Comm. Algebra 22 (1994), no. 8, 3053--3059
Lee, Tsiu-Kwen and Liu, Kun-Shan
Algebras with a finite-dimensional maximal subalgebra
DOI: 10.1081/AGB-200041024
Comm. Algebra 33 (2005), N1, 339-342
Description: If an associative algebra contains a finite-dimensional maximal subalgebra, then it is finite-fimensional.
Availability: G1R9P40872Q63467.pdf
Lee, Donghi
On certain C-test words for free groups
J. Alg. 247 (2002), 509-540
Description: Positive solution to the following problem raised by Shpilrain: There exist two elements u1,u2 in a free m-generated group Fm such that every endomorphism \psi of Fm with non-cyclic image is completely determined by \psi(u1), \psi(u2).
Lee, Min Ho
Lie algebras of formal power series
Rev. Mat. Complut. 20 (2007), no. 2, 463--481
Leedham-Green, C.
Homology in varieties of groups I
TAMS 162 (1971), 1-14
Homology in varieties of groups II
TAMS 162 (1971), 15-25
Homology in varieties of groups III
TAMS 162 (1971), 27-33
Leedham-Green, C. R. and Hurley, T. C.
Homology in Varieties of Groups. IV
DOI: 10.2307/1996312
Transactions of the American Mathematical Society, Vol. 170, Aug., 1972 (Aug., 1972), pp. 293-303
Leep, David B. and Shapiro, Daniel B. and Wadsworth, Adrian R.
Sums of squares in division algebras
Math. Z. 190, 151-162 (1985)
Zentralblatt: 0548.16019
Leeuwen, Marc A. A. van and Roelofs, Marcel
Termination for a class of algorithms for constructing algebras given by generators and relations
Journal of Pure and Applied Algebra Volumes 117-118 , May 1997, Pages 431-445
Leger, G.F.
A note on the derivations of Lie algebras
DOI: 10.2307/2032512
Proc. Amer. Math. Soc. 4 (1953), 511-514
Description: p=0. If Der(Rad(L)) splits over ad(Rad(L)), then Der(L) split over ad(L). (One says that a subalgebra S of a Lie algebra L splits L if L = S + A (direct sum), A is another subalgebra).
Availability: leger.pdf
On cohomology of Lie algebras
DOI: 10.2307/2032674
PAMS 8 (1958), 1010-1020
Description: Action of an ideal on the cohomology of the whole algebra.
Availability: 2.pdf
Derivations of Lie algebras. III
Duke Math. J. 30 (1963), 637-645
Description: If a Lie algebra with nonzero center over p=0 has no outer derivations, then it is not solvable and its radical is nilpotent.
Availability: derIII.pdf
A particular class of Lie algebras
DOI: 10.2307/2033866
PAMS 16 (1965), No.2, 293-296
Description: Lie algebras such that [x,y] in , and, more generally, [x_1, ..., x_k, [x,y] ... ] in .
Availability: 1965-particular.pdf
Leger, George F. and Luks, Eugene M.
On derivations and holomorphs of nilpotent Lie algebras
Nagoya Math. J. 44 (1971), 39-50; Correction and comment: 59 (1975), 217-218
MR 0297828
Zentralblatt: 0264.17003
Cohomology theorems for Borel-like solvable Lie algebras in arbitrary characteristic
CJM 24 (1972), N6, 1019-1026
Zentralblatt: 0272.17004
Description: H^i(B,B) = 0, i >= 1, for (solvable) Borel subalgebra B of a semisimple Lie algebra over p=0. Hochschild-Serre like decomposition for cohomology of a semidirect sum of a Lie algebra and a module in arbitrary characteristic.
Availability: LegLuk72.pdf
On a duality for metabelian Lie algebras
J. Algebra 21 (1972), N2, 266-270
Zentralblatt: 0244.17008
Cohomology and weight systems for nilpotent Lie algebras
BAMS 80 (1974), N1, 77-80
Availability: LegLuk74.pdf
Cohomology of nilradicals of Borel subalgebras
DOI: 10.2307/1996733
TAMS 195 (1974), 305-316
Zentralblatt: 0348.17005
Description: Low-dimensional, in adjoint and close to them modules.
Availability: 1.pdf
Generalized derivations of Lie algebras
DOI: 10.1006/jabr.1999.8250
J. Alg. 228 (2000), N1, 165-203
Zentralblatt: 0961.17010
Description: Construction simultameously generalizing derivations and centroid.
Availability: hardcopy
Leger, G.F. and Manley, P.L.
Dimensionally nilpotent Lie algebras
J. Algebra 117, No.1, 162-164 (1988)
Zentralblatt: 0649.17010
Description: An n-dimensional Lie algebra L having a nilpotent derivation $\Delta$ with $\Delta\sp{n-1}\ne 0$ over p=0 is solvable or simple of dimension 3.
Lehmann, E.L.
Proverka statisticheskikh gipotez
2nd ed., Nauka, 1979
Availability: 1979-proverka.djvu; Kolkhoz' obmennik
Lehmer, D. H.
On the partition of numbers into squares
Amer. Math. Monthly 55(1948), No.8, 476-481
Availability: 2.pdf
Leidwanger, Severine
Basic representations of A_{n-1}^{(1)} and A_{2n}^{(2)} and the combinatorics of partitions
Adv. Math. 141(1999), 119-154
Description: On p.135, a "graph of Young diagrams", very similar to mine, is appearing.
Availability: 1781a.pdf
Leinster, Tom
The Euler characteristic of a category
arXiv:math.CT/0610260
Documenat Math., to apper
The Euler characteristic of a category as the sum of a divergent series
arXiv:0707.0835
Higher Operads, Higher Categories
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Leites, Dmitry
Cohomology of Lie superalgebras
Funct. Anal. Appl. 9 (1975), N4, 75-76
Description: Leites: "This is actually my worst paper. But people keep referring to it though it has nothing but obvious definitions".
Availability: hardcopy
New Lie superalgebras and mechanics
Soviet Math. Dokl. 18 (1977), n.5, 1277-1280
Description: Darboux theorem in super-setting.
Availability: hardcopy
Introduction to the theory of supermanifolds
DOI: 10.1070/RM1980v035n01ABEH001545
Russ. M. Surv. 35 (1980), N1, 1-64
Availability: hardcopy (pages 1-53, 61-64 only); rm1545.pdf
Representations of Lie superalgebras
Theor. Math. Phys. 52 (1982) 764-766 (English)
Teor. Mat. Fiz. 52 (1982) 225-228 (Russian)
Abstract: The description of irreducible representations of sl(1|m) and osp(2|2n). A review of results on irreducible representations.
Teoriya supermnogoobrazii
Petrozavodsk, 1983
Availability: Kolkhoz; petrozavodsk-fr.tar (bunch of msword6 files, unpublished French translation); petrozavodsk.djvu (Russian edition); absent on amazon
Clifford algebra as a superalgebra and quantization
Theor. Math. Phys. 58 (1984), N2, 1984, 229-232
Abstract: A result of C. T. C. Wall on the Brauer group in supersetting is rediscovered. An attempt to quantize antibraket is performed.
Description: Relationship between Clifford superalgebra and Poisson Lie superalgebra.
Availability: H3G934W380J28281.pdf
Lie superalgebras
DOI: 10.1007/BF02249121
VINITI, Vol. 25, 1984, 3-
J. Soviet Math. 30 (1985), 2481-2512
Availability: hardcopy; Kolkhoz
Selected problems of supermanifold theory
DOI: 10.1215/S0012-7094-87-05427-5
Duke Math. J. 54 (1987), 649-656
MR 89c:58014
Zentralblatt: 0646.58012 (Leites: reviewer missed the point)
Availability: 1987-54-manin.djvu (the whole volume)
Towards classification of simple Lie superalgebras
Diff. Geom. Methods in Theor. Physics (ed. L.-L.Chan and W.Nahm), NATO ASI Ser. B, Vol. 245, Plenum, 1990, 633-651
Indecomposable representations of Lie superalgebras
arXiv:math.RT/0202184, 10 p.
Memorial volume dedicated to Misha Saveliev and Igor Luzenko (ed. A.N.Sissakian et al.), JINR, Dubna, 2000, 126-131
On unconventional integrations and cross ratio on supermanifolds
arXiv:math.RT/0202194
Proc. Intern. Workshop "Supersymmetries and Quantum Symmetries" (ed S.Krivonos, J.Lukierski, A.Pashnev), Elsevier, 2002
Description: "... homological fields corresponding to simple Lie algebras and superalgebras are described".
Availability: hardcopy
The Riemann tensor for nonholonomic manifolds
Homology, Homotopy and Applications 4 (2002), 397-407
arXiv:math.RT/0202213
MR 1918518
Zentralblatt: 1015.53012
Description: Structure functions.
Availability: hardcopy
Supersymmetry of the Sturm-Liouville and Korteveg-de Vries operators
Operator Methods in Ordinary and Partial Differential Equations, S.Kovalevski Symposium (ed. S.Albeverio et al.), Birkhauser, 2002, 267-285
Zentralblatt: 1033.37037
Description: Description of "tensor modules"; section 3: relations between H^1, H^2, "symmetric" cohomology, Leibniz cohomology (after Dzhumadildaev), and such.
Availability: KdV-shch.{tex,dvi}
On computer-aided solving differential equations and stability study of markets
Zap. Nauchn. Sem. POMI 312 (2004), 165-187
J. Math. Sci. 133 (2006), No.4, 1464-1476
Zentralblatt: pre02213839
Super K_i-groups for supercommutative superalgebras (after O.Ogievetsky and B.Tsygan)
Manuscript
Description: A survey; Tsygan's K-functor for Lie superalgebras; short review of (ordinary) K-functors. Cohomology of super Poisson algebras extended over super commutative ring (!); lot of open problems.
Availability: Kfun.tex (latex file compiles with few errors); hardcopy
Symmetries wider than supersymmetry: towards noncommutative and nonholonomic geometry. Super Radon transform (after Shander)
Manuscript
Description: Mainly philosophical text.
Availability: toprevSRADON.{tex,dvi}
On representations of finite and compact groups, supergroups and Lie superalgebras with applications to dynamical systems (after Vladimir Arnold, Joseph Bernstein and Alexandre Kirillov)
Manuscript, 50 pp.
Description: Lecture notes.
Availability: kirillov.tar
Primenenie kogomologii algebr Lie v narodnom hozyaistve (in Russian)
Globus. Obshchematicheskii seminar, Vyp. 2, MCCME, 2005; 82-
Availability: Kolkhoz (whole book)
Towards classification of simple finite dimensional modular Lie superalgebras
J. Prime Res. Math. 3 (2007), no.2, 101-110
arXiv:0710.5638
Description: A survey.
Leites, Dmitry and Peiqi, Xuan
Supersymmetry of the Schrodinger and Kortwege-de Vries operators
Manuscript
Availability: KdV-hepth(Peiqi).{tex,dvi}
Leites, Dmitry and Poletaeva, Elena
Analogues of the Riemannian structures for classical superspaces
Contemp. Math. 131, Part I(1992), 603-612
Zentralblatt: 0795.53047
Description: Structure functions
Availability: hardcopy (copy); hardcopy (book)
Supergravities and contact type structures on supermanifolds
Contemp. Math. 184 (1995) (Second Int. Conf. Alg., Barnaul, 1991), 267-274
Zentralblatt: 0847.58008
Description: Structure functions
Availability: hardcopy (copy); hardcopy (book); google books
Defining relations for classical Lie algebras of polynomial vector fields
Math. Scand. 81 (1997), No.1, 5-19
arXiv:math.RT/0510019
Zentralblatt: 0893.17003 0893.17003
Availability: hardcopy
Leites, Dmitry and Poletaeva, E. and Serganova, V.
On Einstein equations on manifolds and supermanifolds
J. Nonlinear Math. Phys. 9(2002), No.4, 394-425
math.DG/0306209
MR 2003i:53037
Zentralblatt: 1009.35085
Description: Structure functions.
Availability: hardcopy
Leites, Dmitry and Premet, Alexander and Shereshevskii, Ilia
The local invariants of flag manifolds
Draft manuscript
Description: H^i for some nilpotent subalgebras of classical Lie algebras with emphasis on H^2; motivated by structure functions.
Availability: sugra(premet).tex
Leites, D.A. and Semenov-Tyan-Shanskii, M.A.
Integrable systems and Lie superalgebras
Zapiski Nauchn. Sem. LOMI 123(1983), 92-97
J. Soviet Math. 20(1985), 525-528
Description: Toda lattices associated to Lie superalgebras?
Availability: 1983-123.djvu (whole Russian journal issue)
Leites, Dmitry and Serganova, Vera
Metasymmetry and Volichenko algebras
Phys. Lett. B 252 (1990), N1, 91-96
Abstract: Simple finite dimensional Volichenko algebras (nonhomogeneous subalgebras of Lie superalgebras) are classified under a technical assumption.
Availability: volich-new.tex (preprint version, under the title "Symmetries wider than supersymmetry and simple Volichenko algebras")
Definig relations for classical Lie superalgebras. I
Topological and Geometrical Methods in Field Theory (eds. J. Mickelsson and P. Peckonnen), World Sci., 1992, 194-201
Leites, Dmitry and Serganova, Vera and Shchepochkina, Irina
Automorphisms and real forms of the simple Lie superalgebras of vector fields
Manuscript
Availability: realf.{tex,dvi}
Leites, Dmitry and Serganova, Vera and Vinel, G.
Symplectic and periplectic supermanifolds
Manuscript
Description: Structure functions; deformations of h(2|2).
Availability: h(2,2,lambda).tex
On cross ratio of four points on "classical superdomains" related with simple Lie superalgebras of polynomial growth
Manuscript
Availability: Jordan.{tex,dvi}
Leites, Dmitry and Sergeev, Alexander
Orthogonal polynomials of a discrete variable and Lie algebras of complex size matrices
URL: http://math.la.asu.edu/~sf2000/sergeev.html http://mi.mathnet.ru/eng/tmf599
DOI: 10.1007/BF02551394
Theor. Math. Phys. 123 (2000), no. 2, 2000, 582--608
arXiv:math.RT/0509528
MR 1794157
Zentralblatt: 1017.17021
Automorphisms and real structures of Lie superalgebras of supermatrices of complex size
Manuscript
Availability: gl(lam)real.{tex,dvi}
Leites, D. and Shapovalov, A.
Manin-Olshansky triples and Lie superalgebras
J. Nonlinear Math. Phys., to appear
Abstract: G.Olshansky showed that for certain simple finite dimensional Lie superalgebras there exist solutions of the quantum Yang-Baxter equation though no classical solutions. The result is generalized to all simple Z-graded Lie superalgebras of polynomial growth.
Leites, Dmitry and Shchepochkina, Irina
How to quantize the antibracket
Theor. Math. Phys. 126(2001), No.3, 281-306 (English)
Teor. Mat. Fiz. 126(2001), No.3, 339-369 (Russian)
Abstract: We show that in contrast to ${\germ po}(2n \mid m)$, its quotient modulo center, the Lie superalgebra ${\germ h}(2n \mid m)$ of Hamiltonian vector fields with polynomial coefficients, has exceptional additional deformations for $(2n \mid m)=(2 \mid 2)$ and only for this superdimension. We relate this result to the complete description of deformations of the antibracket (also called the Schouten or Buttin bracket). It turns out that the space in which the deformed Lie algebra (result of quantizing the Poisson algebra) acts coincides with the simplest space in which the Lie algebra of commutation relations acts. This coincidence is not necessary for Lie superalgebras.
Availability: fulltext.pdf; hardcopy
List of classical Lie superalgebras
Description: (Somewhat chaotic) list of known algebras, their central extensions and deformations
Availability: toward1.tex; hardcopy
The classification of the simple Lie superalgebras of vector fields
Preprint MPI Bonn 2003-28
Description: About vectory (in Leites' terminology) superalgs, that is, over C[[t]], _not_ stringy (over Laurent) ones;
Availability: hardcopy (one of the previous versions - sent by Leites at August 28, 2002); MPI web site; sh.tex (latest version sent by Leites at June 16, 2003)
Deformations and central extensions of the simple Lie superalgebras of polynomial vector fields
planned for Feigin Festschrift
Availability: hardcopy; deform.tex
Classification of the real simple Lie superalgebras of vector fields
planned for Feigin Festschrift ?
Availability: bf2.{tex,dvi}
The Howe duality and Lie superalgebras
Manuscript
Availability: Howe-arw.{tex,dvi}
Quivers and Lie superalgebras
Manuscript
Availability: quivers-Burdik.{tex,dvi}
Leitner, Frederick
Algebraic deformation quantization
math.QA/0605043, 13 pp.
Abstract: In this note we give an algebraic proof of "deformation quantization" by making use of the theory of Unital Gr\"{o}bner bases over a valuation ring.
Lemire, F. and Patera, J.
Gelfand representations of sl(n,C)
AGG 2 (1985), 146-166
Description: With emphasis on sl(2) and sl(3)
Availability: hardcopy
Lemke, F. and Muller, J.-A.
Self-organizing Data Mining for a Portfolio Trading System
Journal of Computational Intelligence in Finance 5(1997), no.3, pp.12-26
Availability: portfolio.pdf
Self-organizing Data Mining
Preprint
Availability: sodm.pdf
Lennox, John C. and Robinson, Derek J. S.
The Theory of Infinite Soluble Groups
Oxford Univ. Press, 2004
Description: Including linear groups.
Availability: Kolkhoz
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Lenstra, Hendrik W. Jr. and Zarhin, Yuri G.
The Tate conjecture for almost ordinary abelian varieties over finite fields
Preprint
Availability: hardcopy
Lepowsky, James
Lectures on classical invariant theory
Brandeis U., typewritten notes, 1971, 76 pp.
Description: Including representations of symmetric and linear groups.
Availability: hardcopy
Generalized Verma modules, loop space cohomology and MacDonald-type identities
Ann. Sci. École Normale Supér. 12 (1979), no.2, 169-234
MR 81a:17004
Zentralblatt: 0414.17007
Description: Cohomology of some Lie algebras (close to loop?).
Some developments in vertex operator algebra theory, old and new
arXiv:0706.4072
Description: A survey.
Lepowsky, James and Li, Haisheng
Introduction to vertex operator algebras and their representations
Progress in Mathematics, 227, Birkhauser, 2004, 318 pp.
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Lepowsky, James and Primc, Mirko
Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$
Contemp. Math. 46 (1985), 84 pp.
Availability: $12
Leron, Uri
Matrix methods in decompositions of modules
Lin. Alg. Appl. 31(1980), 159-171
Abstract: Matrix methods of elementary linear algebra are extended to general direct-sum decompositions of modules. These methods are then shown to yield simple proofs of some well-known theorems, notably the Beck-Warfield "mutual exchange property" and the Krull-Schmidt theorem.
Availability: science.pdf
Leron, Uri and Vapne, Amitai
Polynomial identities of related rings
DOI: 10.1007/BF02771307
Israel Journal of Mathematics Volume 8, Number 2 / June, 1970 Pages 127-137
Description: If A ~ B and A' ~ B~ (where ~ means to have the same identities, then A \otimes B ~ A' \otimes B').
Availability: 1970-polynomial.pdf
Letzter, Edward S.
Effective detection of nonsplit module extensions
DOI: 10.1016/j.jpaa.2004.10.013
J. Pure Appl. Algebra 198 (2005), no.1-3, 225--236
Description: Algorithimic construction of nonsplit modules over finite-dimensional associative algebra
Detecting Infinitely Many Semisimple Representations in a Fixed Finite Dimension
arXiv:0708.3190
to appear in Journal of Algebra
Abstract: ... we describe an algorithmic test for determining whether or not a finitely presented algebra has infinitely many equivalence classes of semisimple representations...
Leur, Johan van de
Twisted toroidal Lie algebras
math.RT/0106119
Abstract: Using $n$ finite order automorphisms on a simple complex Lie algebra we construct twisted $n$-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case $n=2$ we list certain simple Lie algebras and their automorphisms, which produce twisted 2-toroidal algebras. In this way we obtain Lie algebras that are related to all Extended Affine Root Systems of K. Saito.
Levchuk, V.M.
Ueber die Approximierbarkeit freier Gruppen durch die Gruppen PSL(3,q) bei ungeradem q
Seminar Algebraicheskie Sistem. 3 (1970), 71-93 (in Russian)
LeVeque, William Judson
Topics in Number Theory. Vol. I
Addison-Wesley, 1956
Availability: hardcopy
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Levi, D.
Lie symmetries for lattice equations
in: Difference and Differential Equations (ed. Saber Elaydi et al.), AMS, 2004
Levi, D and Negro, J and Olmo, M A del
Discrete q-derivatives and symmetries of q-difference equations
J. Phys. A: Math. Gen. 37 (12 March 2004) 3459-3473
Abstract: In this paper we extend the umbral calculus, developed to deal with difference equations on uniform lattices, to q-difference equations. We show that many properties considered for shift invariant difference operators satisfying the umbral calculus can be implemented to the case of the q-difference operators. This q-umbral calculus can be used to provide solutions to linear q-difference equations and q-differential delay equations. To illustrate the method, we will apply the obtained results to the construction of symmetry solutions for the q-heat equation.
Levi, D. and Winternitz, P.
Continuous Symmetries of Difference Equations
nlin.SI/0502004
Description: A survey about what happens with Lie group symmetries when passing from differential to difference equations.
Levin, J.J. and Schatz, S.S.
Riccati algebras
Duke M.J. 30(1963), 579-594
MR 0159853
Zentralblatt: 0149.27902
Description: (Jordan) algebra of matrices with multiplication A*B = 1/2(APB + BPA).
Availability: 1077374939.pdf
Levinger, J.S.
Nuclear Photo-Disintegration
Oxford Univ. Press, 1960; paperback, 144 pp.
Availability: hardcopy (book)
Levstein, F.
A classification of involutive automorphisms of an affine Kac-Moody Lie algebra
DOI: 10.1016/0021-8693(88)90308-0
J. Alg. 114 (1988), 489-518
Description: Automorphisms of order 2.
Availability: science.pdf; hardcopy (first 10 pages only).
Levy-Nahas, Monique
Deformation and contraction of Lie algebras
DOI: 10.1063/1.1705338
J. Math. Phys. 8 (1967), N6, 1211-1222
Availability: 1967-deformation.pdf; hardcopy
Lévy-Nahas, Monique and Seneor, Roland
First order deformations of Lie algebra representations, E(3) and Poincaré examples
DOI: 10.1007/BF01645689
Comm. Math. Phys. 9 (1968), N3, 242-266
MR 0235804
Zentralblatt: 0161.46003
Description: Simultaneous deformations of a Lie algebra and a module. Seems to be elementary considerations in the Gerstenhaber's spirit, with worked out examples.
Lewin, J.
A matrix representation for associative algebras, I
DOI: 10.2307/1996780
Trans. Amer. Math. Soc. 188 (1974), 293-308
MR 49#2828
Zentralblatt: 0343.16002
Availability: 3.pdf
A matrix representation for associative algebras, II
DOI: 10.2307/1996781
Trans. Amer. Math. Soc. 188 (1974), 309-317
Zentralblatt: 0343.16003
Availability: 4.pdf
Lewis, K.N. and Robinson, M.D. and Hughes, T.R. and Hogue, C.W.V.
MyMED: A database system for biomedical research on MEDLINE data
IBM Systems J. 43(2004), N4, 756-766
Availability: hardcopy
Lewis, David W.
Involutions and anti-automorphisms of central simple algebras
J. Pure Appl. Alg. 182 (2003), N2-3, 253-261
Involutions and anti-automorphisms of algebras
DOI: 10.1112/S002460930601873X
Bull. London Math. Soc. 38 (2006), 529-545
Description: A interesting survey.
Availability: 529.pdf; hardcopy
Lewis, Gene
The integral cohomology rings of groups of order p^3
Trans. Amer. Math. Soc. 132 (1968), No.2, 501-529
Availability: 1968-p3.pdf
Leykin, Anton
Algorithmic proofs of two theorems of Stafford
Journal of Symbolic Computation Volume 38, Issue 6 , December 2004, Pages 1535-1550
Description: Theorem that every left ideal in the Weyl algebra is 2-generated.
Leznov, A.N. and Saveliev, M.V.
Gruppovye metody integrirovaniya dinamicheskikh sistem
(in Russian)
Description: Lie-algebraic methods.
Availability: Kolkhoz
LI, Xiuxian and HOU, Dongping and BAI, Chengming
Rota-Baxter operators on pre-Lie algebras
DOI: 10.2991/jnmp.2007.14.2.9
JNMP 14 (2007), N2, 269-289
Description: (Parametric) generalization of the classical R-matrix equation.
Li, Ke Feng and Lin, Lei
Derivation algebras of variations of Lie algebra $G_2$ in characteristic $2$. (Chinese. English summary)
J. East China Norm. Univ. Natur. Sci. Ed. 2001, no. 3, 1--7
Li, Wanglai and Wilson, Robert L.
Central extensions of some Lie algebras
Proc. Amer. Math. Soc. 126 (1998), 2569-2577
Description: Of Lie algebras of differential operators on C((t)), and C((t)) \otimes C^n.
Availability: ext4.ps; hardcopy
Li, Haisheng
Vertex algebras and vertex Poisson algebras
DOI: 10.1142/S0219199704001264
Comm. Contemporary Math. 6 (2004), No. 1, 61-110
arXiv:math.QA/0209310
A new construction of vertex algebras and quasi-modules for vertex algebras
DOI: 10.1016/j.aim.2005.03.008
Adv. Math. 202 (2006), N1, 232-286
Li, Huishi
Noncommutative Groebner Bases and Filtered-Graded Transfer
LNM 1795 (2002)
The general PBW property
Algebra Colloquium Year: 2007 Vol: 14 Issue: 4 (December 2007) Page: 541 - 554
arXiv:math.RT/0609172
Description: Graded associative algebras. Golod-Shafarevich, homology of Shafarevich's complex associated with presentation.
Algebras and their associated monomial algebras
arXiv:math.RA/0609583
Description: For certain classes of associative algebras, a sort of "associated graded" construction is considered, and lifting of their homological and other properties to an original algebra.
Li, Wanglai
2-cocycles on the algebra of differential operators
J. Algebra 122 (1989), 64-80
MR 90d:17018
Li, Yu
A superalgebraic interpretation of the quantization maps of Weil algebras
DOI: 10.1007/s10114-007-1022-9
Acta Math. Sinica 24 (2008), N2, 285-304
arXiv:math.QA/0502150
Description: Weil algebars (S*(g) \otimes wedge^(g)), their quantizations, homolgical complexes, Duflo isomorphism (S(g) = U(g)), ...
Lian, Haifeng and Tan, Shaobin
Structure and representation for a class of infinite-dimensional Lie algebras
DOI: 10.1016/j.jalgebra.2006.05.013
J. Algebra 307 (2007), N2, 804-828
Description: Derivations and universal central extensions of a Lie algebras structure on so(3) \otimes A with a bracket which is a sum of tensor product of some multiplications on so(3) and A (which makes it close to a loop algebra).
Availability: 2007-structure.pdf
Liao, Ming
Le'vy Processes in Lie Groups
Cambridge Tracts in Mathematics (No. 162), Cambridge Univ. Press, 2006
Lichnerowicz, Andre
Derivations et deformations de certaines algebres de Lie infinies classiques
Publ. Dept. Math. Lyon 13 (1978), N4, 1-26
Description: Of infinite-dimensional Lie algebars of vector fields.
Sur les algebres de Lie locales de Kirillov-Shiga
CRAS 296 (1983), N22, 915-922
Description: Some algebras close to Hamiltonian, Schouten bracket, etc.?
Distinguished essential extensions of infinite dimensional classical Lie algebras
Deformation Theory and Symplectic Geometry, Kluwer, 1997
Lichtenbaum, Stephen and Sweedler, Moss
A Nullstellensatz for higher derivations
J. Algebra 17(1971), 19--24
Lichtenstein, L.
Neuer Entwicklung der Potentialtheorie. Konforme Abbildung.
Encyklopaedie der Mathematischen Wissenschaften, Band II3, Heft 3, Teubner, Leipzig, 1919, 178-377
Availability: hardcopy (book)
Lichtman, A.I.
On subgroups of the multiplicative group of skew fields
PAMS 63 (1977), No.1, 15-16
Description: Question whether the multiplicative group of a division ring contains a free subgroup. It is known (later) that the question is positive when a division ring is finite-dimensional over its center.
On matrix rings and linear groups over a field of fractions of enveloping algebras and group rings. I
DOI: 10.1016/0021-8693(84)90087-5
J. Alg. 88 (1984), 1-37
Description: A sort of Tits alternative for some GL_n(D)'s.
Availability: 1984-matrix.pdf
Free subgroups in linear groups over some skew fields
DOI: 10.1016/0021-8693(87)90177-3
J. Alg. 105 (1987), 1-28
Zentralblatt: 0604.20052
Description: An analogue of Tits alternative for subgroups of GL_n(D), D is a skew field of fractions of U(L). Ultraproducts are employed.
Availability: 1987-free.pdf
The soluble subgroups and the Tits alternative in linear group over rings of fractions of polycylic group. I
DOI: 10.1016/0022-4049(93)90105-3
JPAA 86 (1993), 231-287
Availability: 1993-soluble.pdf
The soluble subgroups and the Tits alternative in linear group over rings of fractions of polycylic group. II
J. Group Theory 2 (1999), 173-189
Lichtman, A.I. and Shirvani, M.
HNN-extensions of Lie algebras
PAMS 125 (1997), N12, 3501-3508
Description: HNN-extensions are constructed, and their properties by analogy with the group case are studied. As corollary, short proofs of theorems about embeddings of Lie algebras into a 2-generated algebra are obtained. Case of Lie p-algebras is also treated.
Availability: S0002-9939-97-04124-5.pdf
Licurgo Santos, Edson Carlos and San Martin, Luiz A. B.
Lie algebras with complex structures having nilpotent eigenspaces
Description: Nijenhuis tensor, etc.
Lie, Sophus
Vorlesungen über Differentialgleichungen mit bekannten infinitesimalen Transformationen (bearbeitet und herausgegeben von Georg Scheffers)
Teubner, Leipzig, 1891
Availability: Kolkhoz
Gesammelte Abhandlungen, Band 3 and 5
B.G.Teubner, Leipzig - H.Aschenhoug & Co., Kristiania, 1922, 1924
Availability: Kolkhoz
Lie, Sophus and Scheffers, Georg
Geometrie der Berürungstranformationen
Teubner, Leipzig, 1896
Availability: Kolkhoz; amazon
Liebeck, Martin W.
Lie algebras, 2-graphs and permutation groups
DOI: 10.1112/blms/12.1.25
Bull. London Math. Soc. 12 (1980), no. 1, 29--33
MR 81f:05095
Zentralblatt: 0429.20006
Description: Some Lie algebras over GF(2) defined on graphs.
Availability: 29.pdf
Lieberherr, K.J. and Xiao, C.
Formal foundations for object-oriented data modeling
IEEE Trans. Knowledge and Data Engineering 1993 Volume: 5, Issue: 3 page(s): 462-478
Availability: 00224198.pdf
Liedl, R. and Niederreiter, G.
Finite Fields
Mir, 1988 (Russian translation from Cambridge U. Press, 1986)
Zentralblatt: 0554.12010
Availability: Kolkhoz
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Liedtke, Christian
Natural Central Extensions of Groups
arXiv:math.GR/0505285
Abstract: We generalise the concept of universal central extensions for perfect groups to arbitrary finite groups.
Liere, Robert van and Leeuw, Wim de
GraphSplatting: Visualizing graphs as continuous fields
IEEE Trans. Visualization Comp. Grpahics 9(2003), N2, 206-
Availability: hardcopy
Liermann, H.
Abbildungen ebener Punktmengen und Gruppenstruktur
Otto Salle Verlag, Frankfurt/M.-Hamburg, 1969; paperback, 53 pp.
Availability: hardcopy (book)
Lim, M. H.
Linear mappings on second symmetric product spaces that Preserve rank less than or equal to one
DOI: 10.1080/03081089008817975
Linear and Multilinear Algebra, Volume 26, Issue 3 February 1990 , pages 187 - 193
Linear transformations on symmetry classes of tensors II
DOI: 10.1080/03081089008817976
Linear and Multilinear Algebra, Volume 26, Issue 3 February 1990 , pages 195 - 205
Lim, Tian Khoon
Arc-transitive homogeneous factorizations, Hamming graphs and affine planes
Research Report 2003/21, U. Western Australia
Availability: hardcopy
Lin, Lei
Derivation algebras of Bernstein-Jordan algebras of dimension five (Chinese)
Chin. Ann. Math., Ser. A 18, No.3, 293-298 (1997)
Zentralblatt: 0880.17021
Lin, Zongzhu and Nakano, Daniel Ken
Algebraic group actions on cohomology theory of Lie algebras of Cartan type
J. Algebra 179 (1996), 852-888
Representations of Hopf algebras arising from Lie algebras of Cartan type
DOI: 10.1006/jabr.1996.6897
J. Algebra 189 (1997), N2, 529-567
Description: Representatiins (particularly, tensor products isomorphisms) of module Cartan type Lie algebras.
Extensions of modules over Hopf algebras arising from Lie algebras of Cartan type
DOI: 10.1023/A:1009917927702
Alg. Repr. Theory 3 (2000), 43-80
Abstract: ... there are no self-extensions of simple modules over restricted Lie algebras of Cartan type.
Lin, Weiqiang and Tan, Shaobin
Central extensions and derivations of the Lie algebras of skew derivations for the quantum torus
Comm. Alg. 33(2005), N11, 3919 - 3938
(me)
Availability: hardcopy
Lincoln, Mark and Towers, David
Frattini theory for restricted Lie algebras
DOI: 10.1007/BF01195370
Arch. Math. 45 (1985), N5, 451-457
Lindberg, Lars
On the doubling of quadratic algebras
Colloq. Math. 100 (2004), no. 1, 119--139
Linde, K.J.
Towards Vertex Algebras of Krichever-Novikov Type, Part I
math.QA/0305428, 21 pages
L'Innocente, S. and Macintyre, A.
Towards decidability of the theory of pseudo-finite dimensional representations of sl_2 k, Part I
Fundamenta Mathematicae, to appear
Linshaw, Andrew R.
The cohomology algebra of the semi-infinite Weil complex
DOI: 10.1007/s00220-006-0062-9
math.QA/0501117
Comm. Math. Phys. 267 (2006), N1, 13-23
(me)
Description: Cohomology of the semi-infinite Weil complex over the Virasoro algebra.
Availability: hardcopy
Lipinski, Z.
Quantization of a loop extended SU(2) affine Kac-Moody algebra
Journal of Mathematical Physics -- April 1996 -- Volume 37, Issue 4, pp. 1662-1667
Lipkin, H.L.
Lie Groups for Pedestrians
North-Holland, 1965; hardcover, 162 pp.
Review: Rutwig on amazon
Availability: hardcopy (book); Kolkhoz
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Lipschutz, S and Spellman, D
An Application of a Group of Olshanskii
ASPECTS OF INFINITE GROUPS. A Festschrift in Honor of Anthony Gaglione (eds. Benjamin Fine, Gerhard Rosenberger and Dennis Spellman), World Sci., 2008
Lipyanski, Ruvim (=Lipjanskii, R.S., =Lipyanskij)
Razreshimye algebry Lie nad polem characteristiki p>0
Uch. Zapiski Latv. Univ. 204 (1974), 72-83 (in Russian)
none
Zentralblatt: none
Certain radicals of linear Lie algebras
Usp. Mat. Nauk 29 (1974), No.3, 211-212
MR 55#430
Zentralblatt: 0356.17013
Ob algebraicheskik elementakh v lineinykh algebrakh Lie
Uch. Zapiski Latv. Univ. 257 (1976), N2, 52-63 (in Russian)
Differential calculus in Lie algebras
Algebra i diskretnaya matematika: prikladnye voprosy informatiki (ed. M. Treimanis), Latviiskii Gos. Univ. Im. P. Stuchki, Riga, 1989, 77-84
MR 91d:17005
Zentralblatt: 0846.58003
Description: Fox-like calculus for Lie algebras, via universal envelopes.
Availability: hardcopycopy
Lipyanski, R. and Plotkin, B.
Automorphisms of categories of free modules and free Lie algebras
math.RA/0502212
Lissner, David
Automorphisms of generalized Witt algebras have fixed points
PAMS 14 (1963), 205-210
Littlewood, Dudley E.
The Theory of Group Characters and Matrix representations of Groups
2nd ed., Oxford Univ. Press, 1950
Availability: 1950-theory.djvu; Kolkhoz
Littlewood, J.E.
A Mathematical Miscellany
Nauka, 1978 (Russian translation from English, 1957); paperback
Availability: hardcopy (book); Kolkhoz' obmennik
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Liu, Dong and Hu, Naihong
Leibniz central extensions on some infinite-dimensional Lie algebras
Comm. Algebra 32 (2004), N6, 2385-2405
Description: Of Lie algebras of differential operators over C[t,t^{-1}], C((t)), Virasoro-like algebras and their q-analogs.
Derivation algebras and 2-cocycles of the algebras of q-differential operators
Comm. Algebra 32 (2004), no. 11, 4387--4413
Leibniz superalgebras graded by finite root systems
arXiv:math.RT/0510544
Leibniz algebras graded by finite root systems
arXiv:math.RT/0510545
Leibniz superalgebras and central extensions
DOI: 10.1142/S0219498806001983
J. of Algebra and Its Applications 5 (2006), No. 6, 765-780
arXiv:math.RT/0510546
Description: Central extension of Leibniz current superalgebras.
Universal central extensions of the matrix Leibniz superalgebras sl (m, n, A)
DOI: 10.1080/00927870701246577
Comm. Algebra 35 (2007), N6, 1814-1823
Availability: google scholar
ON THE TOROIDAL LEIBNIZ ALGEBRAS
Preprint
Liu, Dong and Jiang, Cuipo
The generalized Heisenberg-Virasoro algebra
math.RT/0510543
Liu, Dong and Lin, Lei
On the variations of G_2
Chin. Ann. Math. 24B (2003), N3, 387-394
Description: p=2.
Availability: LiuLin.pdf
On the toroidal Leibniz algebras
DOI: 10.1007/s10114-007-1003-z
Acta Math. Sinica 24 (2008), N2, 227-240
Description: Central extensions, derivations, automorphisms.
Liu, Wende and Liu, Baoling
Derivations from the even parts into the odd parts for Lie superalgebras W and S
math.RA/0509177
Liu, Wende and Su, Yucai and Zhang, Yongzheng
Derivations for the even part of the Hamiltonian superalgebra in positive characteristic
math.RA/0510567
Liu, Wende and Zhang, Yongzheng
Infinite-dimensional modular odd hamiltonian superalgebras
Comm. Alg. 32, N6, 2341-2357
The outer derivation algebras of finite-dimensional Cartan-type modular Lie superalgebras
Comm. Algebra 33 (2005), N7, 2131 - 2146
Finite-dimensional odd Hamiltonian superalgebras over a field of prime characteristic
J. Aust. Math. Soc. 79 (2005), no. 1, 113--130
Comm. Alg. 34 (2006), N10, 3767 - 3784 Automorphism groups of restricted Cartan-type Lie superalgebras
DOI: 10.1080/00927870600862615
Derivations of the even parts for modular Lie superalgebras of Cartan type $W$ and $S$
Internat. J. Algebra Comput. 17 (2007), no. 4, 661--714
Liu, Wende and Zhang, Yongzheng and Wang, Xiuling
The derivation algebra of the Cartan-type Lie superalgebra $HO$
J. Algebra 273 (2004), no. 1, 176--205
Liu, Chia-Hsin
Group algebras with units satisfying a group identity
Proc. AMS 127 (1999), no.2, 327-336
Description: If the group of units of a group algebra of a torsion group satisfies a group identity, then the group algebra satisfies a polynomial identity.
Liu, Dong
Steinber-Leibniz algebras and superalgebras
J. Algebra 283 (2005), N1, 199-221
Description: Universal central extensions of the Leibniz algebra sl(n,D) and Steinberg-Leibniz superalgebra stl(m,n,D) over a dialgebra D.
Liu, Kefeng
Heat kernel and moduli spaces. II
arXiv:dg-ga/9612001
Availability: hardcopy
Liu, Keqin (=Liu, Ke-Qin)
Characterizations of the quantum Witt algebra
DOI: 10.1007/BF00420485
Lett. Math. Phys. 24 (1992), N4, 257-265
Description: The same construction as Hom-Lie algebra defined by Larsson and Silvestrov.
Availability: 1992-characterization.pdf
The Generalizations Of Groups
153 Publishing (?), 2004(2005?)
Description: Engel Theorem for Leibniz algebras?
Tangent-like spaces to local monoids
arXiv:math.RA/0507550
Description: Lie-theory-like passage from local monoid to a so-called local Leibniz algebra (which is a notion weaker than Leibniz algebra).
\xi-groups and Hu-Liu Leibniz algebras
arXiv:math.RA/0512577
Description: Lie-theory-like passage from a so-called linear \xi-group to its tangent space which is a so-called Hu-Liu Leibniz algebra.
Number-like objects and the extended Lie correspondence
arXiv:math.RA/0604179
Abstract: We classify finite dimensional division real associative Z_2-algebras, introduce composition Z_2-algebras, and extend the Campbell-Baker-Hausdorff series and Lie correspondence in the context of linear Hu-Liu Leibniz algebras.
Even (odd) roots and simple Leibniz algebras with Lie factor sl_2
arXiv:math.RA/0701017
Liu, Lishi
Kostant's formula for Kac-Moody Lie algebras
DOI: 10.1016/0021-8693(92)90010-J
J. Algebra 149 (1992), N1, 155-178
Description: Cohomology of minus-algebra of Kac-Moody in irreducible highest weight modules (generalizing Kostant's result about cohomology of nilradical of Borel subalgebra).
Availability: 1992-kostant.pdf
Livernet, Muriel
Homology of the stable algebra of matrices over an A[?]-algebra
Comptes Rendus 329 (1999), 113-116
Description: Leibniz homology of the stable algebra of matrices over A can be expressed in terms of the Hochschild homology of A. This theorem extends the result of Cuvier and Loday proved in the framework of associative algebras.
On a plus-construction for algebras over an operad
K-Theory 18 (1999), 317-337
Description: We prove a analogous to Quillen's plus-construction in the category of algebras over an operad. For that purpose we prove that this category is a closed model category and prove the existence of an obstruction theory. We apply further this plus-construction for the specific cases of Lie algebras and Leibniz algebras which are a noncommutative version of Lie algebras: let sl(A) be the kernel of the trace map gl(A)?A/[A,A], where A is an associative algebra with unit and gl(A) is the Lie algebra of matrices over A. Then the homotopy of slA)+ in the category of Lie algebras is the cyclic homology of A whereas it is the Hochschild homology of A in the category of Leibniz algebras.
Lobanov, Alexey V. and Kryukov, Gregory V. and Hatfield, Dolph L. and Gladyshev, Vadim N.
Is there a twenty third amino acid in the genetic code?
Trends in Genetics Volume 22, Issue 7 , July 2006, Pages 357-360
Description: Answer: unlikely.
Loday, Jean-Louis
Homologies diedrale et quaternionique
Adv. Math. 66 (1987), no.2, 119-148
Une version non commutative des algebres de Lie: les algebres de Leibniz
Enseign. Math. 39 (1993), 269-293
Description: A survey. Including cohomology.
Availability: ensmat_1993_39_a_018.pdf
La renaissance des opérades.
Prebubl. IRMA, 1995, 012
Abstract: To any type of algebras (like associative algebras, Lie algebras, Poisson algebras, Leibniz algebras, $A_\infty$-algebras, etc ...) there is associated an algebraic operad. It is made of all the operations that one can perform on a finite number of variables and of their universal relations. This notion showed up again recently in various fields at the same time (moduli spaces of curves, representations of quantum groups, ``graph-complex" of Kontsevitch). The aim of the paper is mainly to report on a result of V. Ginzburg et M. Kapranov who extended the theory of Koszul duality for associative algebras to algebraic operads.
Description: Probably this is related to possibility to construct "homology of anything" using categories (in words of Gerstenhaber).
Algèbres ayant deux opérations associatives (digèbres)
Prebubl. IRMA, 1995, 017
Description: We give axioms for algebras with two associative operations. This new type of algebra, called ``dialgebra'', is related to Leibniz algebras in a way similar to the relationship between associative algebras and Lie algebras. We define the homology theory of dialgebras which is based on the set of binary trees. The computation of the homology of a free dialgebra shows that the operad associated to the dialgebras is a Koszul operad.
Cup-product for Leibniz cohomology and dual Leibniz algebras
Math. Scand. 77 (1995), 189-196
Description: Perhaps an example of application of Kapranov-Ginzburg ideology to Leibniz algebras.
Availability: pdfconvert.pdf
Kunneth-style formula for the homology of Leibniz algebras
MZ 221 (1996), 41-47
Overview on Leibniz algebras, dialgebras and their cohomology
Fields Inst. Comm., AMS, 17 (1997), 91-102
Description: A survey.
Availability: google books; 1997-overview.tar (pages 91,93-94,96-102 only)
Cyclic Homology
2nd ed., Springer, 1998; hardcover, 513 pp.
Description: Leibniz (co)homology is first defined here.
Availability: hardcopy (book)
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Notes on Koszul duality for associative algebras
2000, 11 pp.
Description: Quadratic algebras, Koszul complexes.
Availability: somewhere on the web (file Koszuldual.ps) (?)
Homotopical syzygies
Une degustation topologique: Homotopy theory in the Swiss Alps, Contemp. Math. 265(2000) , 99-127
Description: For group given by presentation, a free resolution for a trivial module is built.
Availability: author's homepage; hsyams.ps
Dialgebras
URL: http://www-irma.u-strasbg.fr/irma/publications/1999/99014.shtml http://www.math.uiuc.edu/K-theory/0333/
LNM 1763 (2001), "Dialgebras and related topics"
arXiv:math.QA/0102053
Description: Dialgebras / Leibniz algebras = associative algebras / Lie algberas; homological theory for dialgebras and other homological theories; operads and Ginzburg-Kapranov are mentioned, and short survey of that is given in appendix B.
Availability: hardcopy (book)
Algebraic K-Theory and the conjectural Leibniz K-Theory
DOI: 10.1023/B:KTHE.0000018382.90150.ce
K-Theory 30 (2003), 105-127
Abstract: The analogy between algebraic K-theory and cyclic homology is used to build a program aiming at understanding the algebraic K-theory of fields and the periodicity phenomena in algebraic K-theory. In particular, we conjecture the existence of a Leibniz K-theory which would play the role of Hochschild homology. We propose a motivated presentation for the Leibniz K2-group of a field.
Loday, Jean-Louis and Frabetti, A. and Chapoton, F. and Goichot, F.
Dialgebras and Related Operads
LNM 1763 (2001); 133 pp.
Availability: hardcopy (book)
Loday, Jean-Louis and Pirashvili, Teimuraz
Universal enveloping algebras of Leibniz algebras and (co)homology
DOI: 10.1007/BF01445099
Math. Ann. 296 (1993), no.1, 139-158
MR 94j:17003
Description: In the category of Leibniz algebras, any central extension of Virasoro algebra splits. HL_2(sl_n(A)) = HH_1(A), n>4. Relationship between Leibniz and Chevalley-Eilenberg cohomology.
Availability: PPN235181684_0296__0_0.pdf; hardcopy (pp. 139-146 only)
Leibniz representations of Lie algebras
DOI: 10.1006/jabr.1996.0127
J. Algebra 181 (1996), N2, 414-425
Description: Leibniz Ext's between modules.
The tensor category of linear maps and Leibniz algebras
URL: http://www-irma.u-strasbg.fr/irma/publications/1995/95028.shtml http://www-irma.u-strasbg.fr/~loday/jllpub.html
Georgian Math. J. 5 (1998), N3, 263-276
Availability: 95028.dvi
Loday, J.-L. and Quillen, D.
Cyclic homology and the Lie algebra homology of matrices
Comment. Math. Helv. 59 (1984), 565-591
MR 86i:17003
Description: Relationship between cyclic homology of augmented algebra and its augmentation ideal.
Availability: PPN358147735_0059__0_0.pdf
Loday, Jean-Louis and Ronco, Maria
On the structure of cofree Hopf algebras
arXiv:math.QA/0405330
Abstract: We prove an analogue of the Poincare'-Birkhoff-Witt theorem and of the Milnor-Moore theorem for non-cocommutative Hopf algebras. The primitive part of a cofree Hopf algebra is a B-infini-algebra. We construct a universal enveloping functor U2 from B-infini-algebras to 2-associative algebras, i.e. algebras equipped with two associative operations. We show that any cofree Hopf algebra H is of the form U2(Prim H). We take advantage of the simple description of the free 2as-algebra in terms of planar trees to unravel the structure of the operad B-infini.
Lodder, Jerry M.
Rigidity of secondary characteristic classes
arXiv:math.DG/9904131, 15 pages
Abstract: ... the characteristic map from Lie algebra cohomology to de Rham cohomology of the manifold, and prove that if the Leibniz cohomology of the Lie algebra vanishes, then all secondary characteristic classes are rigid. In the case of codimension one foliations (with trivial normal bundle), we show that a characteristic map from the Leibniz cohomology of formal vector fields to the de Rham cohomology of the manifold detects a one-parameter variation of the Godbillon-Vey class.
Leibniz homology, characteristic classes and K-theory
arXiv:math.KT/0106126
Description: If f: A \to B is a homomorphism of algebras, the relative Leibniz homology groups HL_*(f) are defined HL_{*+1}(gl(f)) \to HC_*(f), where HC_*(f) denotes relative cyclic homology, and gl(f): gl(A) \to gl(B) is the induced map on matrices.
From Leibniz homology to cyclic homology
K-Theory 27 (2002), 359-370
Description: A natural homomorphism from Leibniz to Hochschild homology is constructed that is induced by an antisymmetrization map on the chain level. This map is surjective for an algebra gl(A), A an algebra over a characteristic zero field. If f: A -> B is an algebra homomorophism, the relative groups HL*(gl(f)) are studied, where gl(f): gl(A) -> gl(B) is the induced map on matrices.
A comparison of Leibniz and cyclic homologies
aXiv:math.KT/0507165
A characteristic map for symplectic manifolds
arXiv:0801.3446
Description: Leibniz (co)homology of the largest finite-dimensional subalgebra of the Lie algebra of Hamiltonian vector fields.
Lofwall, Clas
On the subalgebra generated by the one-dimensional elements in the Yoneda Ext-algebra
Algebra, algebraic topology and their interactions, Proc. Conf., Stockholm 1983, Lect. Notes Math. 1183 (1986), 291-338
MR 88f:16030
Zentralblatt: 0595.16020
Lofwall, C. and Roos, J.-E.
Cohomologie des algebras de Lie gradues et series de Poincare-Betti non-rationelles
CRAS 290 (1980), 733-736
MR 87d:17003
Zentralblatt: 0449.13011
Description: Hochschild-Serre spectral sequence and probably other (co)homological constructions for Lie superalgebras.
A nonnilpotent 1-2-presented graded Hopf algebra whose Hilbert series converges in the unit circle
DOI: 10.1006/aima.1997.1667
Adv. Math. 130 (1997), N2, 161-200
Availability: science-3.pdf
Loh, Wei-Liem
Estimating covariance matrices. II
DOI: 10.1016/0047-259X(91)90055-7
J. Multivar. Anal. 36 (1991), N2, 163-174
Availability: 1991-estimating.pdf
Estimating the Common Mean of Two Multivariate Normal Distributions
DOI: doi:10.1214/aos/1176347983
Ann. Statist. Volume 19, Number 1 (1991), 297-313
Description: Estimation of covariance matrix, group of affine transformations.
Lohmus, J and Paal, E and Sorgsepp, L
Nonassociative algebras in physics
Hadronic Press Monographs in Mathematics, 1994
About nonassociativity in mathematics and physics
DOI: 10.1023/A:1005854831381
Acta Appl. Math. 50 (1998), N1-2
Description: An interesting historical paper.
Loke, Hung Yean
Exceptional Lie algebras with $S_4$ structures over $\Bbb Z$
Int. Math. Res. Not. 2004, no. 63, 3391--3408
Description: An alternative Tits' second construction.
Lombardo, Sara and Mikhailov, A. V.
Reduction groups and automorphic Lie algebras
Comm. Math. Phys. 258 (2005), no. 1, 179--202
Description: Some esotheric explictly defined by structure constants Lie algebras, quasi-graded in Krichever-Novikov sense.
Availability: w1573v4k70j67434.pdf
Long, Ling and Yang, Yifan
A short proof of Milne's formulas for sums of integer squares
Int. J. Number Theory 1(2005), No.4, 533-551
Zentralblatt: 1084.11012
Availability: S1793042105000364.pdf
Longobardi, P. and Maj, M. and Rhemtulla, A.H.
Groups with no free subsemigroups
DOI: 10.2307/2154822
Trans. Amer. Math. Soc. 347 (1995), 1419-1427
MR 95g:20043
Availability: 1995-groups.pdf
Lopes Moreira da Veiga, Maria Helena
Forecasting volatility using a continuous time model
Unitat de Fonaments de l'Ana`lisi Econo`mica (UAB) and Institut d'Ana`lisi Econo`mica, Working paper, 2003.
Abstract: This paper evaluates the forecasting performance of a continuous stochastic volatility model with two factors of volatility (SV2F) and compares it to those of GARCH and ARFIMA models. The empirical results show that the volatility forecasting ability of the SV2F model is better than that of the GARCH and ARFIMA models, especially when volatility seems to change pattern. We use ex-post volatility as a proxy of the realized volatility obtained from intraday data and the forecasts from the SV2F are calculated using the reprojection technique proposed by Gallant and Tauchen (1998).
Are one factor logarithmic volatility models useful to fit the features of financial data? An application to Microsoft data
Unitat de Fonaments de l'Ana`lisi Econo`mica (UAB) and Institut d'Ana`lisi Econo`mica, Working paper, 2003.
Abstract: This paper provides empirical evidence that continuous time models with one factor of volatility, in some conditions, are able to fit the main characteristics of financial data. It also reports the importance of the feedback factor i