) are called thread modules (note that F_{\lambda, \mu) are thread modules). - spectral sequence relating cohomology of L_1 with coefficients in a thread module and with coefficients in trivial module - "glueing" thread modules all this is related to higher Massey product (arising from the cup product on H^*(L_1)).
Availability: hardcopy
Feigin, B. and Jimbo, M. and Loktev, S. and Miwa, T.
Two character formulas for \hat{sl_2} spaces of coinvariants
arXiv:math.QA/0211354, 22 pages
Abstract: We consider $\hat{sl_2}$ spaces of coinvariants with respect to two kinds of ideals of the enveloping algebra $U(sl_2\otimes\C[t])$. The first one is generated by $sl_2\otimes t^N$, and the second one is generated by $e\otimes P(t), f\otimes R(t)$ where $P(t), R(t)$ are fixed generic polynomials. (We also treat a generalization of the latter.) Using a method developed in our previous paper, we give new fermionic formulas for their Hilbert polynomials in terms of the level-restricted Kostka polynomials and $q$-multinomial symbols. As a byproduct, we obtain a fermionic formula for the fusion product of $sl_3$-modules with rectangular highest weights, generalizing a known result for symmetric (or anti-symmetric) tensors.
Feigin, B.L. and Leites, D.A.
New Lie superalgebras of string theories
Group Theoretical Methods in Physics (Zvenigorod 1982), Proceedings, Vol. 3, 623-629
Feigin, B.L. and Leites, D.A. and Serganova, V.V.
Kac-Moddy superalgebras
Group Theoretical Methods in Physics (Zvenigorod 1982), Vol. 3, 631-637
Feigin, B. and Loktev, S.
Cohomology of nilpotent subalgebras of the Lie algebra ^sl_2
DOI: 10.1007/BF02509626
Funct. Anal. Appl. 30 (1996), no.4, 285-287
Description: Cohomology of Lie algebars of the form e_-1 \otimes C[t]f_-1 + e_0 \otimes C[t]f_0 + e_1 \otimes C[t]f_1 where f_i are some polynomials.
Availability: 1996-cohomology.pdf; hardcopy
Multi-dimensional Weyl modules and symmetric functions
Comm. Math. Phys. 251 (2004), no. 3, 427--445
arXiv:math.QA/0212001
Description: Over the current Lie algebra on an affine manifold.
Deformation of Weyl modules and generalized parking functions
IMRN 13388
arXiv:math.QA/0312158
Feigin, Boris and Malikov, Feodor
Fusion algebra at a rational level and cohomology of nilpotent subalgebras of ^sl_2
Lett. Math. Phys. 31 (1994), 315-326
arXiv:hep-th/9310004
MR 96f:17031
Description: A cohomological characterization of admissible representations of Kac-Moody over sl(2).
Modular functor and representation theory of ^sl(2) at a rational level
Contemp. Math. 202 (1997), 357-
Description: Representations of Kac-Moody over sl(2) and of osp(1|2).
Availability: hardcopy (book); fei-mal.{dvi,tex}
Feigin, B. L. and Semikhatov, A. M. and Tipunin, I. Yu.
Equivalence between chain categories of representations of affine sl(2) and N=2 superconformal algebras
arXiv:hep-th/9701043
J. Math. Phys. 39 (1998), 3865-3905
Description: Highest-weight type representation theories of the affine sl(2) and N=2 superconformal algebras are shown to be equivalent modulo the respective spectral flows.
Feigin, Boris and Shoikhet, Boris
On [A,A]/[A,[A,A]] and on a W_n-action on the consecutive commutators of free associative algebra
arXiv:math.QA/0610410
Math. Res. Lett. 14 (2007), no. 5, 781-795
Description: Cyclic homology is a derived functior of A -> A/[A,A]. What happens with A -> A/[A,[A,A]]? And similar questions. As a first step, one need to understand what this quotient is for a free associative algebra A. The Lie algebra W_n acts by outer derivations on some arising algebras.
Feigin, B.L. and Tsygan, B.L.
Additive K-theory and cristalline cohomology
Funk. Anal. Pril. 19 (1985), N2, 52-62
Availability: hardcopy
Additive K-Theory
DOI: 10.1007/BFb0078368
Lect. Notes Math. (K-theory, arithmetic and geometry) 1289 (1987), 67-209
MR 89a:18017
Zentralblatt: 0635.18008
Description: Ch. 4: filtrations of C_*(gl(A))^inv indexed by the partially ordered set of Young diagrams.
Availability: hardcopy
Cyclic homology of algebras with quadratic relations, universal enveloping algebras and group algebras
Lect. Notes Math. (K-theory, arithmetic and geometry) 1289 (1987), 210-239
Availability: hardcopy
Feigin, B.L. and Zelevinsky, A.V.
Representations of contragredient Lie algebars and Kac-Macdonald identities
Availability: feigin.djvu
Feigin, Boris L.
O kogomologiyak algebry Lie polinomialnykh vektornykh polei na pryamoi (in Russian)
Voprosy teorii grupp i gomologicheskoi algebry, 1979, 216-221
Cohomology of groups and algebras of flows
Rus. Math. Surv. 35 (1980), N2, 239-240
Description: (Co)homology (some results are full, some are partial) of g\otimes A for various special A: C[t,t^-1], C[t^1, ..., t^n], R[x], R[[x]], ...
Availability: hardcopy
Cohomology of contact Lie algebras (in Russian)
C. R. Acad. Bulgare Sci. 35 (1982), no. 8, 1029--1031
MR 85b:17012
Zentralblatt: 0517.17005
Semi-infinite cohomology of Kac-Moody and Virasoro Lie algebras
DOI: 10.1070/RM1984v039n02ABEH003112
Rus. Math. Surv. 39 (1984), N2, 155-156
MR 740035
Zentralblatt: 0544.17009|0574.17008
Availability: hardcopy
The Lie algebra gl(\lambda) and the cohomologies of the Lie algebra of differential operators
Usp. Math. Nauk. 43 (1988), No.2, 157-158.
MR 90b:17024
Availability: hardcopy
On the cohomology of the Lie algebra of vector fields and of the current algebra
Selecta Math. Sov. 7 (1988), N1
Availability: hardcopy (both copy and under the "seminar on supermanifolds" red cover)
Conformal field theory and cohomologies of the Lie algebra of holomorphic vector fields on a complex curve
Proc. ICM Kyoto 1990, 71-85
MR 93e:17033
Availability: hardcopy
Differential operators on the moduli space of G-bundles on algebraic curve and Lie algebra cohomologies
Special Functions. ICM Satellite Conf. Proc. (Okayama, 1990), 90-103
MR 93g:17038
Zentralblatt: 0777.17015
Description: Cohomology of g \tensor (polynomials in one even and one odd variable); cohomology of g \tensor C[x]/(x^n); and similiar; spectral sequences, double complexes, etc. Seems to be badly exposed very powerful results.
Availability: hardcopy
Feigin, E.
Infinite fusion products and $\hat{\mathfrak{sl}_2}$ cosets
math.QA/0603226
Description: Tensor products of irreducible representations of affine sl(2).
Feldman, G. and Fulton, T. and Matthews, P.T.
Structure constants for Lie algebras
DOI: 10.1063/1.526300
J. Math. Phys. 25 (1984), 1222-1229
Zentralblatt: 0543.22012
Description: Classical Lie algebras.
Availability: JMathPhys_25_1222.pdf
The semisimple subalgebras of Lie algebras
DOI: 10.1063/1.526301
J. Math. Phys. 25 (1984), 1230-1252
Zentralblatt: 0543.22013
Description: Of semisimple Lie algberas. An approach alternative to those of Dynkin.
Feldman, G.L.
Exact Mayer-Vietoris sequences for free products of Lie algebras with an amalgamated subalgebra (in Russian)
Teoriya otobrazhenii, ee obobshcheniya i prilozheniya. Sbornik nauchnykh trudov, Naukova Dumka, Kiev, 1982, 212-220
MR 85i:17013
Zentralblatt: 0591.17010
Availability: 53660.050116032134.djvu
Ends of Lie algebras
Russ. Math. Surv. 38(1983), No.1, 182-184
MR 84h:17010
Zentralblatt: 0534.17007
Availability: hardcopy
Feldman, G.M.
On the Heyde theorem for discrete Abelian groups
Studia Math. 177 (2006), 67-79
Availability: 2006-heyde.pdf
Feldvoss, Jörg
On the cohomology of restricted Lie algebras
Comm. Alg. 19 (1991), no.10, 2865-2906
MR 92k:17034
Zentralblatt: 0741.17006
Description: Analogues of Schapiro's lemma for restriced cohomology. L is nilpotent iff H^1_*(L,M) = 0 for every irreducible restricted module M not equal K.
Availability: cohresliealg.pdf
A cohomological characterization of solvable modular Lie algebras
Non-Associative Algebra and Its Applications (ed. S. González). Mathematics and Its Applications 303 (1994), Kluwer, 133-139
MR 96d:17018
Zentralblatt: 0817.17023
Description: Vanishing of the first restricted cohomology.
Homological topics in the representation theory of restricted Lie algebras
Contemp. Math. 194 (1996), 69-119
MR 97e:17026
Zentralblatt: 0862.17014
Description: A survey.
Availability: hardcopy (book); google books
Chief factors and the principal block of a restricted Lie algebra
The Monster and Lie algebras. Proceedings of a special research quarter at the Ohio State University (ed. J. Ferrar et al.), de Gruyter, Ohio State Univ. Math. Res. Inst. Publ. 7 (1998), 187-194
Zentralblatt: 0923.17019
Existence of triangular Lie bialgebra structures
DOI: 10.1016/S0022-4049(97)00128-X
J. Pure Appl. Algebra 134 (1999), no.1, 1-14
MR 2000d:17026
Zentralblatt: 0933.17008
Availability: bialg.pdf
On the number of simple modules of a supersolvable restricted Lie algebra.
J. Algebra 230 (2000), no.2, 319-333
MR 2001f:17037
Zentralblatt: 0978.17010
Representations of Lie colour algebras
Hamburger Beiträge zur Mathematik Heft 79 (circa 2000)
Adv. Math. 157 (2001), No.2, 95-137
Zentralblatt: 0998.17032
Description: With emphasis on restricted color algebras. Rudiments of the theory of color Lie algebras are thoroughly presented.
Availability: color.pdf
Existence of solutions of the classical Yang-Baxter equation for a real Lie algebra
Abh. Math. Semin. Univ. Hamb. 71 (2001), 297-304
Zentralblatt: 0994.17009
Existence of triangular Lie bialgebra structures. II
DOI: 10.1016/j.jpaa.2004.10.005
J. Pure Appl. Algebra 198 (2005), N1-3, 151-163
arXiv:math-ph/0409046
On the cohomology of modular Lie algebras
Contemp. Math. 442 (2007), 89--113
arXiv:math.RT/0608525
Abstract: In this paper we establish a connection between the cohomology of a modular Lie algebra and its p-envelopes. We also compute the cohomology of Zassenhaus algebras and their minimal p-envelopes with coefficients in generalized baby Verma modules and in simple modules over fields of characteristic p>2.
Availability: hardcopy
Feldvoss, Jörg and Nakano, Daniel K.
Representation theory of the Witt algebra
J. Algebra 203(1998), no.2, 447-469
MR 99d:17009
Zentralblatt: 0913.17009
Availability: science.pdf; hardcopy
Feldvoss, Jörg and Strade, Helmut
Restricted Lie algebras with bounded cohomology and related classes of algebras.
DOI: 10.1007/BF02567657
Manuscripta Math. 74(1992), no.1, 47-67
MR 92m:17033
Zentralblatt: 0756.17008
Availability: 1992-restricted.pdf
Feller, W.
An Introduction to Probability Theory and Its Applications
URL: http://www.krelib.com/matematika/436 http://www.krelib.com/matematika/437 http://techlibrary.ru/books.htm http://ef12517-2.tu-sofia.bg/Desislav Todorov/Frames/Books/Mathematics/Probability and statistics/
Vol. I, 2nd ed., Vol. II, Wiley, 1966; hardcover, 461+626 pp.
Availability: hardcopy
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Fellouris, Anargyros G. and Matiadou, Lina K.
On the classification of the five-dimensional Lie superalgebras
Conference ``Applied Differential Geometry: General Relativity''---Workshop ``Global Analysis, Differential Geometry, Lie Algebras'', 55-60, BSG Proc., 11, Geom. Balkan Press, Bucharest, 2004
A classification of the five-dimensional Lie superalgebras, over the complex numbers
Math. Balkanica 19 (2005), no. 1-2, 143--154
Classification of the five-dimensional Lie superalgebras over the real numbers
Internat. J. Theoret. Phys. 46 (2007), no. 3, 451--470
Felzenszwalb, B. and Giambruno, A. and Leal, G.
On rings which are sums of two PI-subrings: a combinatorail approach
Pacific J. Math. 209 (2003), N1, 17-30
Feng, Ping and Tsygan, Boris
Hochschild and cyclic homology of quantum groups
Comm. Math. Phys. Volume 140, Number 3 (1991), 481-521.
MR 1130695
Zentralblatt: 0743.17020
Description: A spectral sequence for cohomology of quantum group as a Hopf algebra, arising from filtration by a deformation parameter, whose E_2 is a certain Lie algebra cohomology. Lie bialgebras are involved.
Availability: hardcopycopy (preprint version)
Ferland, Jacques A.
Positive subdefinite matrices
Lin. Alg. Appl. 31(1980), 233-244
Description: Generalization of notion of positive-semidefinitness.
Availability: science.pdf
Fernandes, Rui Loja and Monnier, Philippe
Linearization of Poisson brackets
DOI: 10.1007/s11005-004-0340-4
arXiv:math.SG/0401273
Lett. Math. Phys. 69 (2004), N1-3, 89-114
Description: Related to work of Hermann.
Fernandez, Marisa and Ibanez, Raul and Leon, Manuel de
Poisson cohomology and canonical homology of Poisson manifolds
Archivum mathematicum 32 (1996), No.1, 29-56
The canonical spectral sequences for Poisson manifolds
Israel J.M. 106 (1998), 133-155
Description: (Poisson) cohomology of Poisson algebras
Availability: hardcopy
Fernandez Lopez, Antonio and Garcia, Esther and Gomez Lozano, Miguel
The Jordan socle and finitary Lie algebras
DOI: 10.1016/j.jalgebra.2004.06.013
J. Algebra 280 (2004), N2, 635-654
Inner ideal structure of nearly Artinian Lie algebras
DOI: 10.1090/S0002-9939-08-09607-X
Proc. Amer. Math. Soc. 137 (2009), 1-9
Fernández López, Antonio and García, Esther and Gómez Lozano, Miguel and Neher, Erhard
A construction of gradings of Lie algebras
DOI: 10.1093/imrn/rnm051
Intern. Math. Res. Notices (2007), article rnm051, 34 pages
Abstract: ... we present a method to construct gradings of Lie algebras. It requires the existence of an abelian inner ideal B of the Lie algebra whose subquotient, a Jordan pair, is covered by a finite grid...
Description: Algebras are apparently not necessarily finite-dimensional.
Availability: rnm051.pdf
Fernandez, Luis M. and Martin-Martinez, Laura
Lie algebras associated with triangular configurations
Lin. Alg. Appl. 407 (2005), 43-63
Description: From a structure constants of a Lie algebra some graph-like structure is constructed.
Availability: science.pdf
Fernandez-Ternero, Desamparados and Nunez-Valdes, Juan
Classification of metabelian Lie algebras of maximal rank
C. R. Acad. Sci. Paris 332 (2001), no. 11, 969--974
Ferrar, J.C.
On Lie algebras of type E_6
BAMS 73 (1967), 151-155
Description: Partial results on forms.
Availability: hardcopy
Lie algebras of type E6
1969
On the classification of Freudenthal triple systems and Lie algebras of type E_7
J. Alg. 62 (1980), 276-282
Description: A reproof of an earlier results due to the author about classification of E_7 over number fields.
Availability: hardcopy
Ferrara, S. and Lledo, M. A.
Considerations on super Poincare algebras and their extensions to simple superalgebras.
Rev. Math. Phys. 14 (2002), no. 6, 519--530.
Ferreira, V. O.
Tensor rings under field extensions
J. Algebra 231(1), 342-363 (2000)
Ferreira, V. O. and Goncalves, J. Z. and Mandel, A.
Free symmetric and unitary pairs in division rings with involution
DOI: 10.1142/S0218196705002177
Internat. J. Algebra Comput. 15 (2005), No.1, 15-36
Description: Under which conditions a pair of symmetric elements multiplicatively generate a free subgroup.
Ferreira, L. A. and Olive, D. I. and Saveliev, M. V.
Orthogonal decomposition of some affine Lie algebras in terms of their Heisenberg subalgebras
DOI: 10.1007/BF01017449
Teoret. Mat. Fiz. 102 (1995), no. 1, 17--31
Theoret. and Math. Phys. 102 (1995), no. 1, 10--22
arXiv:hep-th/9411036
MR 96f:170321348617
Zentralblatt: 0852.17021
Description: "Loopization" of Kostrikin-Kostrikin-Ufnarovskii.
Ferrer, J. and Garcia, M. I. and Puerta, F.
Brunowsky Local Form of a Holomorphic Family of Pairs of Matrices
Lin. Alg. Appl. 253(1997), 175-198
Description: Another development of Arnold's theme of versal deformation for pair of matrices under specific group action.
Availability: brunowsky-local-form.pdf
Ferrero, Miguel and Giambruno, Antonio and Polcino Milies, Ce'sar
A note on derivations of group rings
Can. Math. Bull. 38, No.4, 434-437 (1995)
Zentralblatt: 0838.16029
Ferrero, Miguel A. and Haetinger, Claus
Higher derivations of semiprime rings
Comm. Algebra 30(2002), no. 5, 2321--2333
Higher derivations and theorem by Herstein
Quaestiones Mathematicae VOLUME 25 ISSUE 2 (2002), 249-257
Ferrero, M. and Puczylowski, E. R.
On rings which are sums of two subrings
DOI: 10.1007/BF01194866
Arch. Math. 53 (1989), 4-10
Availability: 1989-rings.pdf
Feynman, R.P.
Statistical Mechanics
Addison-Wesley, 1998; paperback, 354 pp.
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Photon-Hadron Interactions
Addison-Wesley, 1998; paperback, 282 pp.
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Fialowski, Alice
On the classification of graded Lie algebras with two generators
Moscow Univ. Math. Bull. 38 (1983), no.2, 76-79
Availability: classif.pdf
Deformations of a Lie algebra of vector fields on the line
Rus. Math. Surv. circa 1982
Availability: hardcopy
An example of formal deformations of Lie algebras
Deformation Theory of Algebras and Structures and Applications, NATO ASI Ser. Ser. C 247 (1988), 375-401
Zentralblatt: 0663.17009
On the cohomology of infinite dimensional nilpotent Lie algebras
Adv. Math. 97 (1993), 267-277
Description: H^1,2(L,L) for finite- and infinite-dimensional L.
Availability: nilpotent.pdf
Versal deformations of Lie algebras
Nonassociative Algebra and Its Applications (ed. R.Costa, A.Grishkov), M.Dekker, 2000, 91-
google books
Global deformations of Lie algebras
Rings, modules, algebras, and abelian groups, Lect. Notes Pure Appl. Math. 236, Dekker, 2004, 177-188
Zentralblatt: 1048.17010 (me)
Availability: hardcopy
The moduli space and versal deformations of three dimensional Lie algebras
Algebras, rings and their representations, World Sci. Publ., 2006, 79--91
Zentralblatt: (me)
Description: Shortened version of another paper by Fialowski-Penkava.
Availability: hardcopy
Fialowski, Alice and Fuchs, Dmitry
Singular deformations of Lie algebras. Example: deformations of the Lie algebra L_1
Topics in singularity theory, Amer. Math. Soc. Transl. Ser. 2, 180, 1997, 77--92
MR 2001c:17035
Construction of miniversal deformations of Lie algebras.
DOI: 10.1006/jfan.1998.3349
J. Funct. Anal. 161 (1999), no.1, 76--110
math.RT/0006117
MR 2000g:17026
Fialowski, Alice and Malikov, Fyodor
Extensions of modules over loop algebras
URL: http://www.cs.elte.hu/~fialowsk/pubs-af/ http://www.jstor.org/pss/2374946
AJM 116 (1994), 1265-1281
Availability: fial-mal.ps
Fialowski, Alice and Mandal, Ashis
Leibniz algebra deformations of a Lie algebra
DOI: 10.1063/1.2981562
arXiv:0802.1263
J. Math. Phys. 49, 093511 (2008) (11 pages)
Description: Leibniz deformations of the 3-dimensional nilpotent Lie algebra.
Fialowski, Alice and Mandal, Ashis and Mukherjee, Goutam
Versal deformations of Leibniz algebras
arXiv:math.QA/0702476
Fialowski, Alice and Millionschikov, Dmitri V.
Cohomology of some N-graded Lie algebras
Uspekhi Mat. Nauk 59 (2004), no. 6(360), 205--206
Cohomology of graded Lie algebras of maximal class
DOI: 10.1016/j.jalgebra.2005.10.031
math.RT/0412325
J. Algebra 296 (2006), N1, 157-176
Description: N-graded (i.e. generalized-nilpotent) infinite-dimensional Lie algebras.
Fialowski, Alice and Montigny, Marc de
Deformations and contractions of Lie algebras
URL: http://stacks.iop.org/0305-4470/38/6335 http://www.ingentaconnect.com/content/iop/jphysa/2005/00000038/00000028/art00006
J. Phys. A 38 (2005), no. 28, 6335--6349
Description: Including of Krichever-Novikov type.
Availability: a5_28_006.pdf
On deformations and contractions of Lie algebras
SIGMA 2 (2006), 048, 10 pages
arXiv:math.RT/0605091
Description: Seems to be mainly repetition of the previous paper.
Fialowski, A. and O'Halloran, J.
A comparison of deformations and orbit closure
Comm. Alg. 18 (1990), 4121-4140
Description: In p=0, formal and analytic rigidity are equivalent.
Availability: hardcopy
Fialowski, Alice and Penkava, Michael
Deformation theory of infinity algebras
J. Algebra 255 (2002), No.1
arXiv:math.RT/0101097
Description: "Deformation theory in a very general setting".
Examples of infinity and Lie algebras and their versal deformations
Geometry and analysis on finite- and infinite-dimensional Lie groups, Banach Center Publ. 55 (2002), 27-42
arXiv:math.QA/0102140
Versal deformations of three dimensional Lie algebras as L_\infty algebras
DOI: 10.1142/S0219199705001702
Comm. Contemp. Math. 7 (2005), No.2, 145-165
arXiv:math.RT/0303346
Zentralblatt: 1075.14007
Strongly homotopy Lie algebras of one even and two odd dimensions
DOI: 10.1016/j.jalgebra.2004.08.023
J. Algebra 283 (2005), N1, 125-148
arXiv:math.QA/0308016
Zentralblatt: 1081.17012
Classification and extensions of L_\infty algebras of one even and two odd dimension
Preprint MPI Bonn 2003 - 61
Examples of miniversal deformations of infinity algebras
arXiv:math.RT/0510325
Extensions of (super) Lie algebras
arXiv:math.RT/0611234
Description: Cohomological interpretation. Deformations of representations.
Availability: hardcopy
Deformations of four dimensional Lie algebras
DOI: 10.1142/S0219199707002344
Comm. Contemp. Math. 9 (2007), No. 1, 41-79
arXiv:math.RT/0512354
Zentralblatt: pre05161551
Formal deformations, contractions and moduli spaces of Lie algebras
DOI: 10.1007/s10773-007-9481-4
Int. J. Theor. Phys. 47 (2008), N2, 561-582
arXiv:math.QA/0702268
The moduli space of 3-dimensional associative algebras
arXiv:0807.3178
Moduli spaces of low dimensional real Lie algebras
DOI: 10.1063/1.2944995
J. Math. Phys. 49 (2008), 073507
Extensions of L_\infty algebras of two even and one odd dimension
DOI: 10.1515/FORUM.2008.034
Forum Mathematicum. Volume 20 (2008), Issue 4, Pages 711-744
Description: Extensions of a super Lie algebra as an L_\infty algebra.
Fialowski, A. and Post, G.F.
Versal deformation of the Lie algebra L_2
U.Twente, Memorandum 1490, 1999
Fialowski, Alice and Schlichenmaier, Martin
Global deformations of the Witt algebra of Krichever-Novikov type
DOI: 10.1142/S0219199703001208
Comm. Contemp. Math. 5 (2003), No.6, 921-945
arXiv:math.QA/0206114
Zentralblatt: (me)
Availability: hardcopy
Global geometric deformations of current algebras as Krichever-Novikov type algebras
DOI: 10.1007/s00220-005-1423-5
Comm. Math. Phys. 260 (2005), no. 3, 579--612
arXiv:math.QA/0412113
Global geometric deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebra
DOI: 10.1007/s10773-007-9383-5
Internat. J. Theoret. Phys. 46 (2007), no. 11, 2708--2724
arXiv:math.QA/0610851
Fialowski, Alice and Wagemann, Friedrich
Cohomology and deformations of the infinite dimensional filiform Lie algebra m_0
DOI: 10.1016/j.jalgebra.2007.09.004
J. Algebra 318 (2007), N2, 1002-1026
arXiv:math.RT/0703383
Description: Of Lie algebra [e_1,e_i] = e_(i+1), i>=2.
Cohomology and deformations of the infinite-dimensional filiform Lie algebra m_2
DOI: 10.1016/j.jalgebra.2008.02.035
J. Algebra 319 (2008), N12, 5125-5143
arXiv:0708.0363
Zentralblatt: pre05304612 (me)
Availability: hardcopy
Fiedler, Bernd
An algorithm for decomposition of ideals of semi-simple rings and its application to symbolic tensor calculations by computer
Habilitationsschrift, Univ. Leipzig, 1999
Generators of algebraic covariant derivative curvature tensors and Young symmetrizers
arXiv:math.CO/0310020
Chapter for a book "Progress in Computer Science Research", Nova Science Publ, in press
Abstract: We show that the space of algebraic covariant derivative curvature tensors R' is generated by Young symmetrized tensor products W*U or U*W, where W and U are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2),(3)}, {(2),(2 1)} or {(1 1),(2 1)}. Each of the partitions (2), (3) and (1 1) describes exactly one symmetry class, whereas the partition (2 1) characterizes an infinite set S of irreducible symmetry classes. This set S contains exactly one symmetry class S_0 whose elements U can not play the role of generators of tensors R'. The tensors U of all other symmetry classes from S\{S_0} can be used as generators for tensors R'. Foundation of our investigations is a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins about a Young symmetrizer that generates the symmetry class of algebraic covariant derivative curvature tensors. Furthermore we apply ideals and idempotents in group rings C[Sr], the Littlewood-Richardson rule and discrete Fourier transforms for symmetric groups Sr. For certain symbolic calculations we used the Mathematica packages Ricci and PERMS.
Short formulas for algebraic covariant derivative curvature tensors via algebraic combinatorics
arXiv:math.CO/0312171
Description: Young diagrams, symbolic computations.
Fiedorowicz, Z.
The symmetric bar construction
Preprint
Abstract: We show that the cyclic bar construction, a contravarinat functor on the cyclic category, extends to a covarinat functor on the symmetric category, which we all the symmetric bar construction. This enables us to define symmetric homology for algebras, which we compute in the case of group algebras.
Availability: symbar.ps
Fieker, Claus and Graaf, Willem de
Constructing algebraic Lie algebras
math.RA/0611414
Description: An algorithm for constructing the algebraic hull of a given matrix Lie algebra in characteristic zero.
Figueroa-O'Farrill, José
N=2 structures on solvable Lie algebras: The c=9 classification
DOI: 10.1007/BF02102433
Communications in Mathematical Physics Volume 177, Number 1 / March, 1996 Pages 129-156
arXiv:hep-th/9412008
MR 1382223
Zentralblatt: 0864.17007
Description: "An intruging connection" between R-matrices and complex structures (usual R[Rx,y] + ..., etc.)
A geometric construction of the exceptional Lie algebras F4 and E8
DOI: 10.1007/s00220-008-0581-7
Comm. Math. Phys. 283 (2008), N3, 663-674
arXiv:0706.2829
Figueroa-O'Farrill, Jose M. and Stanciu, Sonia
On the structure of symmetric selfdual Lie algebras
J.Math.Phys. 37(1996), 4121-4134
hep-th/9506152
Description: Lie algs possessing invariant symmetric nondegenerate bilinear form.
Filippov, V.T.
Zero divisors and nil elements in Mal'tsev algebras
DOI: 10.1007/BF01668424
Algebra and Logic 14 (1975), N2, 124-131
Availability: 1975-zero.pdf
Mal'cev algebras satisfying Engel's condition
DOI: 10.1007/BF01669005
Algebra and Logic 14 (1975), N4, 271-281
Availability: 1975-malcev.pdf
On engelian Mal'tsev algebras
DOI: 10.1007/BF01875932
Algebra and Logic 15 (1976), N1, 57-71
Availability: 1976-engelian.pdf
Central simple Mal'tsev algebras
DOI: 10.1007/BF01877239
Algebra and Logic 15 (1976), N2, 147-151
The Lie center of binary-Lie algebras
DOI: 10.1007/BF01668598
Algebra and Logic Volume 16, Number 2 / March, 1977 Pages 143-153
Generalization of alternative and Mal'tsev algebras
DOI: 10.1007/BF01670125
Algebra and Logic 17 (1978), N1, 75-87
Availability: 1978-generalization.pdf
A class of simple nonassociative algebras
DOI: 10.1007/BF01158719
Math. Notes 45 (1989), N1, 68-71
Availability: 1989-class.pdf
Lie center of semiprime binary-Lie algebras
DOI: 10.1007/BF00970488
Siber. Math. J. 32 (1991), N3, 490-495
Availability: 1991-lie.pdf
Binary Lie algebras without strong zero divisors
DOI: 10.1007/BF01978835
Algebra and Logic 30 (1991), N2, 149-166
The "measure of non-Lieness" for Malcev algebras
DOI: 10.1007/BF02259852
Alg. and Logic 31 (1992), 198-217
Availability: 1992-measure.pdf
Annihilators of Mal'tsev algebras
DOI: 10.1007/BF00739573
Algebra and Logic 33 (1994), N5, 322-334
Description: Malcev algebras with Engel condition.
Lie algebras satisfying identities of degree 5
DOI: 10.1007/BF00739334
Algebra and Logic 34 (1996), N6, 379-394
Abstract: Let F be an associative ring with unity, containing 1/6. We prove that every prime Lie F-algebra satisfying the identity [(yx)(zx)]x = 0 is embedded as a subring of a special form in a three-dimensional simple Lie algebra over some field. It follows that there exists no central simple Lie algebra which is not three-dimensional and the cube of every inner derivation in which is a derivation.
Description: Antiderivations of an anticommutative algebra A are maps D:A->A satisfying D(xy) = -D(x)y - xD(y). A prime Lie algebra having a nonzero antiderivation satisfies the standard identity of degree 5.
Availability: 1996-lie.pdf
On \delta-derivations of Lie algebras
DOI: 10.1007/BF02674132
Siber. Math. J. 39 (1998), N6, 1218-1230
Description: delta-derivations are maps D:A->A such that D(xy) = delta (D(x)y + xD(y). Relation with R-matrix. In almost all cases, prime Lie algebras do not have delta-derivations. Every prime Lie algebra having an anti-derivation (delta = -1) is 3-dimensional simple.
Availability: 1998-delta-derivations.pdf
On \delta-derivations of prime Lie algebras
Dokl. Math. 59 (1999), No.1, 79-80
Dokl. Akad. Nauk 364 (1999), No.4, 453-454
Zentralblatt: 0977.17015
\delta-derivations of prime Lie algebras
DOI: 10.1007/BF02674305
Siber. Math. J. 40 (1999), N1, 174-184
Zentralblatt: 0936.17021
Simple Sagle algebras
DOI: 10.1007/BF02675366
Math. Notes 65 (1999), no.4, 506--509
Zentralblatt: 0969.17001
Description: An arbitrary finite-dimensional simple Sagle algebra over a field of characteristic zero is a Lie algebra (this solves question 3.90 from the Dniester notebook). Result in char. p.
Availability: hardcopy
Binary Lie algebras satisfying the third Engel condition
DOI: 10.1007/s11202-008-0071-3
Siber. Math. J. 49 (2008), N4, 744-748
Description: They are locally nilpotent and cannot be semiprime.
Fine, B. and Roehl, F. and Rosenberger, G.
The Tits alternative for generalized triangle groups
Groups Korea 98, DeGruyter, 2000, 95-132
Finkelberg, M.
Graded Brauer group
Seminar on Supermanifolds (ed. Leites), 1987
Description: Brauer group in color setting.
Availability: FINKEL-1.{tex,dvi}
Finston, David R.
On multiplication algebras
DOI: 10.2307/2000039
Trans. Amer. Math. Soc. 293 (1986), No.2, 807-818
Description: Multiplication algebra of the tensor product of algebras. Characterization of semisimple multiplication algebras. Examples.
Availability: 1986-multiplication.pdf
Endomorphisms and null subalgebras of finite dimensional algebras revisited
Arch. Math. 54 (1990), 352-357
Description: Results about infinity and dimension of the group of automorphisms of not necessarily associative algebras. p>0 and Lie algebras are given special attention.
Availability: u317r81030284751.pdf
Fiore, Marcelo and Leinster, Tom
Objects of categories as complex numbers
math.CT/0212377
Adv. Math. Volume 190, Issue 2 , 30 January 2005, Pages 264-277
Availability: hardcopy
Fiorenza, Domenico and Ionescu, Lucian M.
Graph Complexes in Deformation Quantization
Letters in Mathematical Physics Issue: Volume 73, Number 3 Date: September 2005 Pages: 193 - 208
Fischbacher, Thomas
Introducing LambdaTensor1.0 - A package for explicit symbolic and numeric Lie algebra and Lie group calculations
hep-th/0208218, 10 pages
AEI-2002-065
Abstract: Due to the occurrence of large exceptional Lie groups in supergravity, calculations involving explicit Lie algebra and Lie group element manipulations easily become very complicated and hence also error-prone if done by hand. Research on the extremal structure of maximal gauged supergravity theories in various dimensions sparked the development of a library for efficient abstract multilinear algebra calculations involving sparse and non-sparse higher-rank tensors, which is presented here.
Fishel, Susanna and Grojnowski, Ian and Teleman, Constantin
The strong Macdonald conjecture
arXiv:math.RT/0107072
Description: Cohomology of current Lie algebras; notes about Feigin's papers.
The strong Macdonald conjecture and Hodge theory on the loop grassmannian
arXiv:math.AG/0411355
Ann. Math., to appear
Description: Substantial expansion of the previous paper.
Availability: hardcopy
Fisher, John R.
Axiomatic radical and semisimple classes of rings
Pacific J. Math. 97 (1981), N1, 81-91
MR 638174
Zentralblatt: 0466.16008, 0451.16004
Description: Radicals of ultraproducts.
Fisman, Elsa
Finite factorizable groups
PhD Thesis, Bar-Ilan U., 1982, 73 pp.
Availability: hardcopy (book)
On the product of two finite solvable groups
DOI: 10.1016/0021-8693(83)90008-X
J. Algebra 80 (1983), N2, 517-536
Products of solvable subgroups of a finite group
DOI: 10.1007/BF01198714
Archiv der Mathematik Volume 61, Number 3 / September, 1993 Pages 201-205
Description: Refs to works on finite groups representable as the product of solvable subgroups.
Fitelson, Branden
Likelihoodism, Bayesianism, and Relational Confirmation
Synthese, to appear
Description: Philosophical issues of likelihood.
Flanders, H.
Differential Forms with Applications to the Physical Sciences
Dover, 1989; paperback, 205 pp.
Availability: hardcopy (book)
Flanigan, Francis J.
Algebraic geography: variety of structute constants
Pacific J. Math. 27 (1968), 71-79
MR 0237573
Zentralblatt: 0165.35001
Description: Not every associative algebra deforms into a rigid one. An accurate exposition of question of orbits, rigidity, etc.
Straightening-out and semirigidity in associative algebras
TAMS 138 (1969), 415-425
MR 38:5855
Zentralblatt: 0176.31102
Availability: 11.pdf
Which algebras deform into a total matrix algebra?
DOI: 10.1016/0021-8693(74)90115-X
J. Alg. 29 (1974), N1, 103-112
Zentralblatt: 0276.16026
Description: Approach via idempotents.
Availability: 1974-deform.pdf
On Levi factors of derivation algebras and the radical embedding problem
Pacific J. Math. 57 (1975), no. 2, 371--378
MR 53#10877
Zentralblatt: 0334.17003
Description: p=0, alg. cl. Every direct sum of classical simple Lie algebras of types A-D is a Levi factor of DerN for some nilpotent associative algebra N.
Availability: 1975-levi.pdf
On the ideal and radical embedding of algebras. II. Nilpotent radicals
DOI: 10.1016/0021-8693(79)90109-1
J. Algebra 60 (1979), 76-95
Zentralblatt: 0419.16014
Description: Associative algebras.
Availability: 1979-radical.pdf
Flath, Daniel
THE CLEBSCH-GORDAN FORMULAS
L'Enseignement Mathématique / Volume 29 (1983), 339-346
Description: Through the Weyl algebra.
Flato, M. and Gerstenhaber, M. and Voronov, A.A.
Cohomology and deformation of Leibniz pairs
arXiv:q-alg/9502006
Lett. Math. Phys. 34 (1995), 77-90
Zentralblatt: 0844.17015
Description: A cohomology theory of pairs (L, A), where L is Lie algebra acting as derivations on associative commutative algebra A (and, as particular case Poisson algebras), is developed; double complexes; deformations. nothing more than very generic homological reasonings.
Availability: hardcopy
Flato, M. and Lichnerowicz, A. and Sternheimer, D.
Deformations of Poisson brackets, Dirac brackets and applications
DOI: 10.1063/1.523104
J. Math. Phys. 17 (1976), N9, 1754-1762
Availability: JMathPhys_17_1754.pdf; hardcopy
Flato, M. and Sternheimer, D.
Star products, quantum groups, cyclic cohomology, and pseudodifferential calculus
in: Contemp. Math. (AMS) 175(1984)
Quantum groups, star products and cyclic cohomology
Quantum and Non-Commutative Analysis. Kluwer, 1993
Fletcher, William T.
On Whitehead's second lemma for Lie algebras
DOI: 10.1155/S016117128200060X
Intern. J. Math. Math. Sci. 5 (1982), N3, 621-623
Description: An elementary proof not dependent on the first Whitehead lemma.
Flüge, Ruedi and Ruh, Ernst A.
Barycenter and maximum likelihood
Diff. Geom. Appl. 24 (2006), N6, 660-669
DOI 10.1016/j.difgeo.2006.08.009
Description: Lie groups.
Foissy, L.
E'tude de l'alge`bre de Lie double des arbres enracine's de'core's
DOI: 10.1016/j.aim.2006.04.002
Advances in Mathematics Volume 208, Issue 2 , 30 January 2007, Pages 877-904
Abstract: The double Lie algebra LD of rooted trees decorated by a set D is introduced, generalising the construction of Connes and Kreimer. It is shown that it is a simple Lie algebra. Its derivations and its automorphisms are described, as well as some central extensions. Finally, the category of lowest weight modules is introduced and studied.
Availability: sdarticle.pdf
Fokkinga, Maarten M.
Calculate categorically!
CWI Report CS-R9132, 1991
Formal Aspects of Computing 4(1992), N4, 673-692
Description: "computations instead of diagram chasing" in the framework of category theory
Availability: hardcopy
Folly, Y.
Sur la rigidité des représentations de sl(2)
Rend. Semin. Fac. Sci. Univ. Cagliari 67 (1997), 1-8
Zentralblatt: 0939.17006
Description: Lie algebras of the form sl(2) + Rad, where Rad as sl(2)-module is a sum of two irreducibles, are examined for rigidity. Some of those rigid Lie algebras have nonvanishing cohomology.
Fomenko, A.T. and Trofimov, V.V.
Integrable systems on Lie algebras and symmetric spaces
Advanced Studies in Contemporary Mathematics. 2, Gordon and Breach, N.Y., 294 p. (1989)
Zentralblatt: 0742.58001
Fomenko, Anatolii T.
Mathematical Impressions
AMS, 1990; big format, hardcover, dustjacket; 184 pp.
Availability: hardcopy (book)
Differencialnaya geometriya i topologiya. Dopolnitelnye glavy
2nd ed., Regular & Chaotic Dynamics, 1999 (in Russian); paperback, 249 pp.
Availability: hardcopy (book)
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Novye emiriko-statisticheskie metodiki datirovaniya drevnikh sobytii i prilozheniya k globalnoi khronologii dervnego i srednevekovogo mira
Fomenko, O.M.
Distribution of lattice points on certain second-order surfaces
DOI: 10.1007/BF02439206
Zap. Nauchn. Semin. POMI 212, 164-195 (1994)
J. Math. Sci., New York 83, No.6, 795-815 (1997)
Zentralblatt: 0861.11055
Description: Sums of squares?
Availability: fulltext.pdf
Fong, C. K. and Miers, C. R. and Sourour, A. R.
Lie and Jordan ideals of operators on Hilbert space
DOI: 10.2307/2044026
PAMS 84 (1982), No. 4, 516-520
Availability: 1982-lie.pdf
Fordy, A.P.
A historical introduction to solitons and Baecklund tranformations
Harmonic maps and integrable systems (ed. A.P. Fordy and J.C. Wood), Vieweg, 1994, 7-
Forger, Michael and Sachse, Sebastian
Lie superalgebras and the multiplet structure of the genetic code. I. Codon representations
J. Math. Phys. 41(2000), 5407-5422
math-ph/9808001
Availability: hardcopy
Lie superalgebras and the multiplet structure of the genetic code. II. Branching rules
J. Math. Phys. 41(2000), 5423-5444
Forster, Malcolm and Sober, Elliott
Why Likelihood?
The Nature of Scientific Evidence (ed. M. Taper and S. Lele), Univ. of Chicago Press, 2004, 153-165
Description: Largely philosophical.
Forsythe, George E. and Leibler, Richard A.
Matrix Inversion by a Monte Carlo Method
Mathematical Tables and Other Aids to Computation, Vol. 4, No. 31 (Jul., 1950), pp. 127-129
Description: A von Neumann-Ulam method; also allows to get element(s) of inverted matrix without calulating the whole matrix.
Fosback, N.G.
Stock Market Logic
Dearborn Financial Publ., 21st printing, 1992; softcover, 384 pp.
Availability: hardcopy (book)
Foulkes, H. O.
Further analysis of R. A. Fisher's enumerations in genetics
Biometrics 21 (1965), No.4, 1012-1015
Availability: 1965-enum.pdf
FOULLEY, J. L.
A Simple Argument Showing How to Derive Restricted Maximum Likelihood
1993 J Dairy Sci 76:2320-2324
Description: Some matrix derivation operations aiming to get maximum likelihood estimates from multivariate-normal-distribution related situation.
Availability: 2320.pdf
Fournelle, T.A. and Weston, K.W.
Generalizations of Steinberg groups
Series in Algebra. 4. Singapore: World Scientific. xiii, 230 p.
Zentralblatt: 0914.20029
Description: Seems to be a generalization of Malcev's correspondance between groups and rings/Lie algebras using words. Interesting.
Fowels, G.R. and Cassiday, G.L.
Analytical Mechanics
6th ed., Saunders College Publ., 1999 (?); hardcover, 484 pp.
Availability: absent on amazon; hardcopy (book)
Fox, Ralph H.
Free differential calculus. I. Derivation in the free group ring.
Ann. Math. 57 (1953), N3, 547-560
Availability: fox1-low.pdf; hardcopy
Free differential calculus. II. The isomorphism problem of groups.
Ann. Math. 59 (1954), N2, 196-210
Availability: fox2.pdf; hardcopy
Free differential calculus. III. Subgroups.
Ann. Math. 64 (1956), N3, 407-419
Availability: fox3.pdf; hardcopy
Free differential calculus. V. The Alexander matrices re-examined.
Ann. Math. 71 (1960), N3, 408-422
Availability: fox5.pdf; hardcopy
Fox, Thomas F.
Jump deformations and triple cohomology
J. Alg. 105(1987), 437-442
Availability: hardcopy
Frabetti, Alessandra
Leibniz homology of dialgebras of matrices
J. Pure Appl. Alg. 129 (1998), 123-141
Dialgebra (co)homology with coefficients
URL: http://www-irma.u-strasbg.fr/irma/publications/1997/97039.shtml http://math.univ-lyon1.fr/~frabetti/papers/homoabs.html
Prepubl. IRMA, 1997, 039
Lect. N. Math. 1763 (2001)
Frabetti, Alessandra and Wagemann, Friedrich
On the Leibniz cohomology of vector fields.
Ann. Global Anal. Geom. 21 (2002), no. 2, 177--190
arXiv:math/0005126
Fradkin, E.S. and Linetsky, V.Ya.
Virasoro like infinite dimensional superalgebras: analytic continuations of simple Lie algebras
Preprint TECHNION-PH-90-36, Jun 1990. 15pp.
Proc. 18th Int. Colloq. on Group Theoretical Methods in Physics, Moscow, Jun 4-9, 1990
A new class of infinite-dimensional Lie algebras: an analytical continuation of the arbitrary finite-dimensional semisimple Lie algebra
DOI: 10.1142/S021773239000130X
Mod. Phys. Lett. A 5 (1990), 1167-1174
Franjou, Vincent and Friedlander, Eric M.
Cohomology of bifunctors
DOI: 10.1112/plms/pdn005
Proc. London Math. Soc. 97 (2008), N2, 514-544
Description: Starts with simple linear algebra and quickly proceeds to cohomological abstarct nonsense. Related to cohomology of linear groups.
Frank, Marguerite
Two new classes of simple Lie algebras
Trans. AMS 112(1964), No.3, 456-482
Zentralblatt: 0134.27002
Availability: 0.pdf
Restrictedness and simplicity in Lie algebras of characteristic p
Scripta Math. 29, 395-407 (1973)
Zentralblatt: 0285.17010
A new simple Lie algebra of characteristic three
Proc. Am. Math. Soc. 38, 43-46 (1973)
Zentralblatt: 0237.17004
Franses, P.H.
Periodicity and Stochastic Trends in Economic Time Series
Oxford Univ. Press, 1996; softcover, 230 pp.
Availability: hardcopy (book)
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Frappat, L. and Ragoucy, E. and Thuillier, F.
GENERAL CONSTRUCTION OF THE VIRASORO ALGEBRA FROM SUPERALGEBRAS
Preprint LAPP-TH-326-91, Feb 1991. 13pp
Phys.Lett.B262:271-277,1991
Frappat, Luc and Sciarrino, Antonio and Sorba, Paul
Dictionary of Lie Algebras and Superalgebras
Academic Press, 2000, 410pp.
arXiv:hep-th/9607161, 145pp (preliminary preprint version under different title)
Description: Structure and (finite-dimensional) representations.
Availability: dictionary.pdf
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A crystal base for the genetic code
arXiv:physics/9801027
Availability: hardcopy (with defects)
Symmetry and codon usage correlations in the genetic code
arXiv:physics/9812041
Availability: hardcopy
Crystalizing the genetic code
arXiv:physics/0003037
Description: Evolution of genetic code is modelled after quantum enveloping algebra U_q(sl(2) + sl(2)).
Availability: hardcopy (with defects)
Sum rules for codon usage probabilities
arXiv:physics/0205013
Availability: hardcopy
Corelation matrix for quartet codon usage
arXiv:cond-mat/0304326
Availability: hardcopy
Fraser, D. A. S.
Statistical Models and Invariance
Ann. Math. Statist. Volume 38, Number 4 (1967), 1061-1067
Description: Statistical models invariant under Lie group action.
Frazer, W.R.
Elementary Particles
Prentice-Hall, 1966; hardcover, 190 pp.
Freese, W.
Einige unitäre Darstellungen der Virasoro-Algebra
Hamburger Beitraege zur Math, Heft 70
Frege, G.
Die Grundlagen der Arithmetik
Reclam, 1987; paperback, small format, 159 pp.
Availability: hardcopy (book)
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Fregier, Yael
A new cohomology theory associated to deformations of Lie algebra morphisms
DOI: 10.1007/s11005-004-4289-0
arXiv:math.QA/0304323
Lett. Math. Phys. 70 (2004), N2, 97-107
Availability: hardcopy
Deformation of the Heisenberg algebra inside gl(3,K)
arXiv:math.RT/0403410, 15 pages
Freidman, P.A.
Rings with a right idealizer condition
Ural. Gos. Univ. Mat. Zap. 4(1963), 51-58
MR 32#1215
Description: rings in which every subring is a right ideal.
Freifeld, Charles
The cohomology of transitive filtered modules. I: The first cohomology group
DOI: 10.2307/1995293
Trans. Amer. Math. Soc. 144 (1969), 475-491
Description: Filtered modules over filtered (infinite-dimensional) Lie algebras.
Availability: 0-150.pdf
Frenkel, Edward
Vertex algebras and algebraic curves
Seminaire Bourbaki 1999-2000, N875
Availability: bourbaki.pdf
Frenkel, E. and Ben-Zvi, D.
Vertex Algebras and Algebraic Curves
1st ed. AMS, 2001; 2nd ed., AMS, 2004
Availability: Kolkhoz (1st ed.)
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Frenkel, I.B. and Garland, H. and Zuckerman, G.J
Semi-infinite cohomology and string theory
Proc. Nat. Acad. Sci. USA 83 (1986), 8442-8446
Frenkel, Igor and Huang, Y.Z. and Lepowsky, James
On axiomatic approaches to vertex operator algebras and modules
Mem. Amer. Math. Soc. 494 (1993), 64 pp.
MR 94a:17007
Zentralblatt: 0789.17022
Availability: Lbs-Hbs Ţjóđarbókhlađa, Tímarit án stađsetningar. 52 (1965),83 (1968),181- (1977-) and also in VR-II: 512.55 Fre; 1993-axiomatic (pages v-vi,1,9-13,21-22,27-31,33-34,42,64 only)
google books
Frenkel, Igor and Khovanov, Mikhail and Stroppel, Catharina
A categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products
arXiv:math.QA/0511467
Frenkel, Igor and Libine, Matvei
Quaternionic analysis, representation theory and physics
DOI: 10.1016/j.aim.2008.03.021
arXiv:0711.2699
Advances in Mathematics Volume 218, Issue 6, 20 August 2008, Pages 1806-1877
Frenkel, Igor and Malkin, Anton and Vybornov, Maxim
Affine Lie algebras and tame quivers
math.TR/0005119
Description: P.Gabriel's celebrated 1972 Manuscripta Math. paper about representations of quivers and Dynkin diagrams was aftewards generalized by Bernstein-Gelfand-Ponomarev via some reflection functors related to a Weyl group of a corresponding classical Lie algebra. Here this is pushed further, to affine root systems.
Availability: hardcopy
Frenkel, Igor B. and Styrkas, Konstantin
Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology
math.QA/0409117
Adv. Math. 206 (2006), N1, 57-111
Frenkel, Edward and Teleman, Constantin
Self-extensions of Verma modules and differential forms on opers
math.QA/0401428
Compositio Mathematica 142 (2006), 477-500
Description: Cohomology of current Lie algebras.
Frenkel, Igor and Wang, Weiqiang
Virasoro algebra and wreath product convolution
arXiv:math.QA/0006087
Description: Group-theoretic construction of the Virasoro algebra in the framework of wreath products.
Frenkel, I.B. and Zhu, Y.
Vertex operator algebras associated to representations of affine and Virasoro algebras
DOI: 10.1215/S0012-7094-92-06604-X
Duke Math. J. 66 (1992), N1, 123-168
MR 1159433
Zentralblatt: 0848.17032
Availability: 1992-vertex.pdf
Fresse, Benoit
Koszul duality of operads and homology of partition posets
math.AT/0301365, 144 pages
Homotopy theory and its applications (Evanston, 2002), Contemp. Math. 346 (2004), 115-215
Abstract: We consider partitions of a set with $r$ elements ordered by refinement. We consider the simplicial complex $\bar{K}(r)$ formed by chains of partitions which starts at the smallest element and ends at the largest element of the partition poset. A classical theorem asserts that $\bar{K}(r)$ is equivalent to a wedge of $r-1$-dimensional spheres. In addition, the poset of partitions is equipped with a natural action of the symmetric group in $r$ letters. Consequently, the associated homology modules are representations of the symmetric groups. One observes that the $r-1$th homology modules of $\bar{K}(r)$, where $r = 1,2,...$, are dual to the Lie representation of the symmetric groups. In this article, we would like to point out that this theorem occurs a by-product of the theory of \emph{Koszul operads}. For that purpose, we improve results of V. Ginzburg and M. Kapranov in several directions. More particularly, we extend the Koszul duality of operads to operads defined over a field of positive characteristic (or over a ring). In addition, we obtain more conceptual proofs of theorems of V. Ginzburg and M. Kapranov.
Freund, J.E.
Modern Elementary Statistics
3rd ed., Prentice-Hall, 1967; hardcover, 432 pp.
Availability: hardcopy (book)
Frey, Gabriel and Michel, Christian J.
An analytical model of gene evolution with six mutation parameters: An application to archaeal cirular codes
Comput. Biology and Chemistry 30(2006), 1-11
Availability: science.pdf
Fried, E.
Automorphism group of integral domains fixing a given subring
DOI: 10.1007/BF02485446
Algebra Universalis 7 (1977), 373-387
Description: Each group is a suitable automorphism group.
Availability: fulltext-4.pdf
Fried, M.
A note on automorphism groups of algebraic number fields
Proc. AMS 80 (1980), No.3, 386-388
Description: Every finite group is an automorphism group of an algebraic field extension of Q.
Availability: 1980-aut.pdf; hardcopy
Friedland, S.
Matrices with prescribed off-diagonal elements
Israel J.M. 11(1972), 184-189
Description: There exists an n x n matrix over algebraically closed field, all of whose eiegenvalues and off-diagonal elements are prescribed. The number of such matrices is finite.
Friedlander, Eric M. and Parshall, Brian J.
Cohomology of Lie algebras and algebraic groups
DOI: 10.2307/2374473
Amer. J. Math. 108 (1986), 235-253
Zentralblatt: 0601.20042
Description: Probably relation between modular and Z_p-cohomology (via spectral sequence?).
Availability: 2374473.pdf
Limits of infinitesimal group cohomology
Algebraic topology and algebraic K-theory, Ann. Math. Stud., Princeton Univ., 113(1987), 523-538
Zentralblatt: 0708.20012
Description: Something about relations between Z_p- and rational cohomology of algeberaic groups (defined over Z_p)
Availability: google books; 1987-limits.tar (many pages are missing)
Modular representation theory of Lie algebras
DOI: 10.2307/2374686
Amer. J. Math. 110 (1988), No.6, 1055-1093
Availability: 0-150.pdf; hardcopy
Deformations of Lie algebra representations
DOI: 10.2307/2374747
Amer. J. Math. 112 (1990), 375-395
Description: Lie algebras of reductive algebraic groups over p>0. This is _not_ general cohomological deformations in Gerstenhaber sense.
Availability: 0.pdf
Friedman, J.
Computing Betti numbers via combinatorial Laplacians
Algorithmica 21(1998), 331-346
Availability: hardcopy
Friedman, Jerome and Hastie, Trevor and Tibshirani, Robert
Sparse inverse covariance estimation with the lasso
arXiv:0708.3517
Description: Some approaches and references that could be useful in the problem of estimation of covariance matrix.
Frobenius, G.
Teoriya charakterov i predstavlenii grupp
Gos. Nauchno-Tekhn. Izdat. Ukrainy, Kharkov, 1937 (collection of Russian translations of papers)
Availability: Kolkhoz; absent on amazon
Froberg, R. and Loofwal, C.
Koszul homology and Lie algebras with applications to generic forms and points
URL: http://www.math.su.se/reports/2000/8/ http://projecteuclid.org/Dienst/UI/1.0/Display/euclid.hha/1139852464
HHA 4(2002), 227-258
Description: Some another version of Koszul homology/resolution.
Frohardt, Daniel E. and Griess, Robert L.
Automorphisms of modular Lie algebras
Nova J. Algebra Geom. 1 (1992), N4, 339-345
Availability: autG.pdf
Frohlich, A.
Baer-invariants of algebras
TAMS 109(1963), 221-244
Frölicher, A. and Bucher, W.
Calculus in Vector Spaces Without Norm
Mir, 1970 (Russian translation from LNM 30(1966)); paperback, 168 pp.
Availability: hardcopy (book); amazon; absent on ozon
Frolicher, Alfred and Nijenhuis, Albert
A theorem on stability of complex structures
Proc. Nat. Acad. Sci. USA 43 (1957), 239-241
Description: Deformations.
Availability: hardcopy
Frucht, Roberto
Herstellung yon Graphen mit vorgegebener abstrakten Gruppe
Compositio Math., 6, 239-250 (1938)
Description: Everey finite group is the automorphism group of a graph.
Graphs of degree three with a given abstract group
Canadian J. Math. 1(1949), 365-378
Description: Further restrictions on graph realizing automorphisms of any given finite group.
Frutiger, Theodore Kimble
A Comprehensive Survey of the Development of Group Theory from Its Inception Until 1900
PhD Thesis, Penn State Univ., 1966
Availability: Kolkhoz
Fu, Jiayuan and Zhang, Qingcheng and Jiang, Cuipo
The Cartan-type modular Lie superalgebra KO
Comm. Algebra 34 (2006), N1, 107-128
Description: Of contact type. Derivations.
Fuchs, Dmitry and Lang, Lynelle (=Lang Weldon)
Massey brackets and deformations
DOI: 10.1016/S0022-4049(99)00159-0
J. Pure Appl. Algebra 156 (2001), 215-229
arXiv:q-alg/9602024
Description: Massey products, cohomology of differential graded Lie algebras, deformations.
Availability: hardcopy
Fuchs, D.B. and Leites, D.
Cohomology of Lie superalgebras
C. R. Acad. Bulg. Sci. 37, 1595-1596 (1984)
Zentralblatt: 0586.17005
Description: cohomology of classical finite-dimensional Lie superalgebras with trivial coefficients
Fuchs, Dmitry and Wilmarth, Constance
Laplacian spectrum for the nilpotent Kac-Moody Lie algebras
DOI: 10.3842/SIGMA.2008.059
arXiv:0808.0890
SIGMA 4 (2008), 059, 11 pages
Description: (Co)chain complexes.
Fuchs, Dmitry B.
Finite-dimensional Lie algebras of formal vector fields and characteristic classes of homogeneous foliations
DOI: 10.1070/IM1976v010n01ABEH001678
Math. USSR Izv. 10 (1976), 55-62
Description: Properies of the map H^*(W_n) -> H^*(L), where L is a finite-dimensional subalgebra of W_n.
O raskrytii skobok, ob Eilere, Gausse, Macdonalde i ob upushchennykh vozmozhnostyakh
Kvant 1981, N8
Stable cohomologies of a Lie algebra of formal vector fields with tensor coefficients
DOI: 10.1007/BF01076720
Funct. Anal. Appl. 17 (1983), N4, 295-301
O stikhotovrnykh razmerakh (in Russian)
Kvant 1988 (?)
Cohomology of Infinite-Dimensional Lie Algebras
College Press, Univ. of Beijing, 1998 (reprint of the Consultants Bureau, 1986
English translation); paperback, small format, 339 pp.
Zentralblatt: 0592.17011
Availability: hardcopy (book); cohomology.djvu [no pages 36-53] (Russian original, Nauka, 1984)
Finite dimensionality of the homology of the Lie algebra of Hamiltonian vector fields on the plane
Funct. Anal. Appl. 19 (1985), 305-310
Availability: hardcopy
Two projections of singular vectors of Verma modules over the affine Lie algebra A_1
Funct. Anal. Appl. 23 (1989), N2, 154-156
MR 90m:17031
Singular vectors over the Virasoro algebra and extended Verma modules
Unconventional Lie Algebras, Adv. Soviet Math. 17, AMS, 1993, 65-74
MR 95b:17031
Availability: hardcopy (in books)
Fuchs, J.
Affine Lie Algebras and Quantum Groups
Cambridge U. Press, corrected paperback edition, 1995; 433 pp.
Availability: hardcopy (book); google books
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Fuchs, L.
Partially Ordered Algebraic Systems
Mir, 1965 (Russian translation from Pergamon Press, 1963); hardcover, 342 pp.
Availability: hardcopy (book); absent on amazon; Kolkhoz (in Russian)
Infinite Abelian Groups. Vol. I, II
Mir, 1974
Availability: Vol. I - Kolkhoz, Vol. II - Kolkhoz' obmennik
Fukshansky, Anna
The sum of two locally nilpotent rings may contain a free non-commutative subring
PAMS 128 (1999), N2, 383-386
Description: Ditto for Lie algebras.
Availability: S0002-9939-99-05005-4.pdf
Fulton, W.
Young Tableaux
2nd corrected printing, Cambridge Univ. Press, 1999; paperback, 260 pp.
Availability: hardcopy (book); Kolkhoz (Russian edition); Euler's library (Russian edition)
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Fulton, William and MacPherson, Robert
A compactification of configuration spaces
Ann. Math. 139 (1994), 183-225
Availability: hardcopy
Furuya, Takahiko and Sanada, Katsunori
Hochschild cohomology of an algebra associated with a circular quiver
Comm. Algebra 34 (2006), no. 6, 2019--2037
Futorny V.
Irreducible graded A_1^(1)-modules
Funct. Anal. Prilozh. 26(1992), N4, 73-75
Availability: hardcopy
Representations of Affine Lie algebras
Queen's Papers in Pure and Applied Mathematics, v. 106, 1997, 89p.
Futorny, Vyacheslav and Kashuba, Iryna
Verma type modules for toroidal lie algebras
DOI: 10.1080/00927879908826677
Communications in Algebra, Volume 27, Issue 8 1999 , pages 3979 - 3991
Zentralblatt: 0940.17011
Description: Totoidal algebars are understood ad universal central extensions of loop algebras.
Futorny, Vyacheslav and Ovsienko, Serge
Kostant theorem for special filtered Lie algebras
math.RA/0303372
Description: A famous Kostant's theorem that U(L) is a free module over its center for classical simple L, proved for a loop algebra over gl(n). Koszul complexes are involved.
(re)generated at Thu Oct 9 20:14:53 GMT 2008
