some bibliography: B

[A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [U] [V] [W] [X] [Y] [Z] [NOAUTHORS]

Babai, L.

On the minimum order of graphs with given group
Canad. Math. Bull. 17 (1974), 467-470
Description: Some special graphs realizing automorphisms of any given finite group.

Babenko, I.K.

Problems of growth and rationality in algebra and topology
DOI: 10.1070/RM1986v041n02ABEH003243
Rus. Math. Surv. 41 (1986), N2, 117-175
Description: p.164- Hochschild-Serre spectral seq. for Lie superalgebras, and related constructions (pairing, etc.) in the case of abelian ideal.
Availability: UVA

Bachmuth, S. and Mochizuki, H.

Triples of 2x2 matrices which generate free groups
DOI: 10.2307/2042030
Proc. AMS 59 (1976), No. 1, 25-28
Availability: 1976-triples.pdf

Backelin, Jörge and Cojocaru, Svetlana and Colesnicov, Alexander and Ufnarovski, Victor

Problems in Interaction with the Computer Algebra System BERGMAN
Computational Commutative and Non-Commutative Algebraic Geometry S. Cojocaru et al. (Eds.) IOS Press, 2005, 185-
Availability: 2005-computational-commutative-and-noncommutative-alg-geom.pdf (whole volume)

Backhouse, Nigel

A classification of four-dimensional Lie superalgebras
J. Math. Phys.19 (1978), 2400-2402
MR 80c:17004
Zentralblatt: 0421.17002

Backhouse, R.

Mathematics of Program Construction. An Introduction
Draft, 2001
Availability: math-progr-constr.djvu

Badawi, Ayman

R_n Contains a Division Ring iff R Does
The American Mathematical Monthly, Vol. 100, No. 7 (Aug. - Sep., 1993), pp. 679-680

Baehr, H. C. and Dimakis, A. and Mu"ller-Hoissen, F.

Differential Calculi on Commutative Algebras
hep-th/9412069

Baer, R.

Situation der Gruppen und Strukture der Gruppe
Sitzungsber. Heidelberg Akad. 2 (1933), 12-17
Description: A (finite nonabelian) group is called hamiltonian, if all its proper subgroups are normal. Th. A Hamiltonian group is representable as the direct product of group of quaternions, an abelian groups of exponent 2, and an abelian group whose elements are of odd order.

Amer. J. Math. 61 (1939), 1-44
Description: If lattices of subgroups of two groups are isomorphic, are then the groups isomorphic ?

Baez, John C.

The Octonions
math.RA/0105155
Bull. Amer. Math. Soc. 39(2002), 145-205.
Description: A big (nice) survey, including constructions of exceptional Lie algebras.
Availability: hardcopy (journal)

Euler characteristic versus homotopy cardinality
slides of some talk, 2003
Description: (De)categorification; question how to unify Euler and "homotopy" characteristics.
Availability: Baez's site; hardcopy

Baez, John C. and Crans, Alissa S.

Higher-dimensional algebra VI: Lie 2-algebras
math.QA/0307263
Theory and Applications of Categories 12(2004), No. 15, 492-528
Description: Lie 2-algebras (categorification of Lie algebras) are described in terms of 3rd cohomology of (ordinary) Lie algebras.

Baez, John C. and Crans, Alissa S. and Stevenson, Danny and Schreiber, Urs

From loop groups to 2-groups
arXiv:math/0504123
Homology, Homotopy and Applications 9 (2007), No. 2, 101-135
Description: The recurring theme of 2-something and H^3.

Baez, John C. and Dolan, James

Higher-dimensional algebra and topological quantum field theory
arXiv:q-alg/9503002
J. Math. Phys. 36 (1995) 6073-6105
Description: Methodological remarks about "weaking" of algebaric structures (Kapranov et al., operads?).

Categorification
Higher Category Theory (ed. E. Getzler and M. Kapranov), Contemp. Math. 230 (1998), 1-36
arXiv:math/9802029

From finite sets to Feynman diagrams
arXiv:math.QA/0004133
Mathematics Unlimited - 2001 and Beyond (eds. Bjorn Engquist and Wilfried Schmid)
Description: Categorification.
Availability: hardcopy

Baez, John C. and Shulman, Michael

Lectures on n-categories and cohomology
arXiv:math.CT/0608420
Description: The relationship between 2-categories and 3rd cohomology is touched. (p. How 2-cohomology and deformations fit the picture (speculative and interesting). "Deformations are just special kind of extension" (p.34)

Baeza-Vega, R. and Catalán, A. and Costa, R.

Bernstein algebras with associative bilinear forms
DOI: 10.1007/BF01292922
Archiv der Mathematik Volume 58, Number 3 / March, 1992 Pages 234-238

Bagci, Irfan and Boe, Brian D. and Chastkofsky, Leonard and Connell, Benjamin and Jones, Benjamin and Li, Wenjing and Nakano, Daniel K. and Platt, Kenyon J. and Shin, Jae-Ho and Wright, Caroline B.

Cohomology of quantum groups: An analog of Kostant's Theorem
arXiv:0809.0838

Bagger, Jonathan and Wess, Julius

Supersymmetry and Supergravity
Princeton University Press, 1992
Description: Bernstein's recommendation as a useful introduction to the supersymmetry.

Bahturin, Yuri A.

Polinomialnye tozhdestva v universalnykh obertyvayushchikh algebrakh
UMN circa 1972, 201-202
MR 52#10829
Zentralblatt: 0276.17003
Description: p>0 (the case p=0 was considered earlier by Latyshev)
Availability: hardcopy

The approximation of Lie algebras
Mat. Zametki 12 (1972), 713-716
Math. Notes 12 (1972), 868-870
MR 47#3476
Zentralblatt: 0249.17015
Description: When an infinite-dimensional Lie algebra is approximated by finite-dimensional ones.

Identities in the universal envelopes of Lie algebras
J. Austral. Math. Soc. 18 (1974), 19-27

Simple Lie algebras satisfying a nontrivial identity
Serdica Bulg. Math. Publ. 2 (1976), N3, 241-246
MR 56#5671
Zentralblatt: 357.17013
Availability: hardcopy

Identities of two variables in Lie algebra sl(2,k)
Trudy Seminara Petrovskogo 5 (1979), 205-208 (Russian)
Contemp. Soviet Math., Petrovskii Seminar 5, Topics in Modern Math., Plenum, 1985, 259-263 (English)
MR 81d:17013 (549629.pdf)
Zentralblatt: absent
Availability: present in bookshops (amazon etc.)

Identical Relations in Lie Algebras
Nauka, 1985
VNU Science Press, 1987
Zentralblatt: 0571.17001
Availability: hardcopy (photocopy); google books

Identities in the universal enveloping algebra for a Lie superalgebra
DOI: 10.1070/SM1986v055n02ABEH003010
Math. USSR Sbornik 55 (1986)
Mat. Sbornik 127 (1985), 384-397
MR 798383
Zentralblatt: 0579.17005
Description: Criteria for U(L) to be a PI-algebra.

Identities of algebras with actions of Hopf algebras
Methods in Ring Theory (ed. V.S. Drensky et al.), Lect. Notes Pure Appl. Math, Marcel Dekker, 198 (1998), 1-36
Zentralblatt: 0948.16017
Description: A unifying review on identical relations in algebras graded by finite groups, invariant rings, algebras with involution, etc.

Actions on algebras and applications
Matematica Contamporanea 20 (2001), 71-153
Zentralblatt: 1004.16032
Description: A survey; among the themes: PI algebras, Lie superalgebras (PI envelopes, generalization of Scheunert's "supertrick")
Availability: journal web site; 20_2.ps; hardcopy

Bahturin, Yu. A. and Baranov, Aleksandr A. and Zalesskii, Aleksandr E.

Simple Lie subalgebras of locally finite associative algebras
DOI: 10.1016/j.jalgebra.2004.06.006
J. Algebra 281 (2004), no.1, 225-246
Zentralblatt: 1104.17014

Bahturin, Yuri and Fischman, Davida and Montgomery, Susan

Bicharacters, twistings, and Scheunert's theorem for Hopf algebras
J. Algebra 236 (2001), No.1, 246-276
Zentralblatt: 0966.17017
Description: Generalization of the Scheunert's "color Lie algebras twisting" in the Hopf algebras setting.

Bahturin, Yuri and Giambruno, Antonio and Riley, David M.

Group-graded algebras with polynomial identity
Isr. J. Math. 104, 145-155 (1998)
Zentralblatt: 0920.16010
Description: If R_e in group-graded associative ring is PI, then the whole ring is PI.

Bahturin, Yuri A. and Kegel, O.H.

Universal sums of abelian subalgebras
DOI: 10.1080/00927879508825381
Comm. Algebra 23 (1995), no.8, 2975-2990
MR 96g:16033
Zentralblatt: 0837.16020
Description: Sum of two (infinite-dimensional) abelian Lie algebras is metabelian.
Availability: 713240930.pdf

Sums of simple subalgebras
DOI: 10.1007/BF02366343
J. Math. Sci. 93 (1999), no.6, 830-835
MR 2000f:16026
Zentralblatt: 0938.16009
Description: Structure of associative algebras which are a sum of two simple subalgebras; in particular, they cannot be simple.

Bahturin, Yu.A. and Mikhalev, A.A. and Petrogradsky, V.M. and Zaicev, M.V.

Infinite Dimensional Lie Superalgebras
de Gruyter Exp. Math. vol.7, de Gruyter, 1992
Zentralblatt: 0762.17001
Description: Color Lie algebras.
Availability: Bahturin.pdf; google books

a
m
a
z
o
n

Bahturin, Yuri and Mikhalev, Alexander A. and Zaicev, Mikhail

Infinite-dimensional Lie superalgebras
Handbook of Algebra (ed. M.Hazewinkel), Vol. 2, Elsevier, 2000, 580-
Description: A survey. Among all, a lucid few-line explanation of the "Scheunert supertrick".
Availability: vol2.djvu; hardcopy

Bahturin, Yuri and Montgomery, Susan

PI-envelopes of Lie superalgebras
Proc. Amer. Math. Soc. 127 (1999), 2829-2839
Zentralblatt: 1027.17024
Abstract: In this paper we find necessary and sufficient conditions on a finite-dimensional Lie superalgebra under which any associative PI-envelope of it is finite-dimensional. We also extend M. Scheunert's result which enables one to pass from color Lie superalgebras to the ordinary ones, to the case of gradings by an arbitrary abelian group.
Availability: S0002-9939-99-04825-X.ps; hardcopy

Bahturin, Y. and Nabiev, S.

Automorphisms and derivations of abelian extensions of some Lie algebras
Abh. Math. Sem. U. Hamburg 62 (1992), 43-57
Zentralblatt: 0780.17020
Availability: hardcopy

Bahturin, Yu.A. and Olshanskii, A.Yu.

The approximation and characteristic subalgebras of free Lie algebras
Trudy Sem. Petrovskogo 2 (1976), 145-150
MR 56#5670
Description: A free non-abelian Lie algebra over an infinite field with some additional property is approximated by any infinite set of nonisomorphic forms of the classical simple Lie algebras. Degrees of identities of classical Lie algebras.
Availability: 75939.050115190459.djvu

Identities
Algebra II: Noncommutative rings. Identities, Encycl. Math. Sci., Vol. 18, Springer, 1991, 107-221
Sovrem. Probl. Mat., Fundam. Napravleniya 18, VINITI, 1988, 117-240
Zentralblatt: 0725.16002
Availability: hardcopy (book)

Large restricted Lie algebras
DOI: 10.1016/j.jalgebra.2006.12.018
J. Algebra 310 (2007), N1, 413-427
arXiv:math.RA/0608764
Zentralblatt: pre05144400
Description: A Lie algebra is called large if there is a subalgebra of finite codimension admitting a surjective homomorphism on a nonabelian free Lie algebra. Generators and relations.

Bahturin, Yu.A. and Pagon, D.

Cohomologies of certain Lie algebras with an abelian ideal
DOI: 10.1070/RM1993v048n03ABEH001035
Russ. Math. Surv. 48 (1993), No.3, 181-182
Zentralblatt: 0856.17023
Zbl Review: If $Q$ belongs to some variety $V$, then it is possible to study deformations in the variety $V$. In the paper cohomologies of Lie algebras with an abelian ideal with coefficients in the adjoint module are considered. For $Q=L/R^2$, $R \triangleleft L$, $G=L/R$, $A=R/R^2$ the isomorphism $H^{n-1} (G,H^1(A,Q)) \cong H^{n+1} (G,A)$ is established. Rigidity of any free metabelian Lie algebra in the variety of metabelian algebras is proved.
Availability: rm_48_181.pdf

Bahturin, Y. and Pagon, D. and Zaicev, M.

Rigidity of free algebras in varieties of Lie algebras
Comm. Algebra 24 (1996), N12, 3719-3724
MR 97j:17004
Zentralblatt: 0860.17006
Availability: hardcopy

Bahturin, Yuri and Petrogradsky, Victor

Polynomial identities of smash producsts
URL: http://www.heldermann.de/JLT/JLT12/JLT122/jlt12021.htm http://www.emis.de/journals/JLT/vol.12_no.2/4.html
J. Lie Theory 12 (2002), 369-395
Zentralblatt: 1014.17006
Description: Development on the theme of polynomial identities of group algebras and universal enveloping algebras.

Bahturin, Y. A. and Sehgal, S. K. and Zaicev, M. V.

G-identities of non-associative algebras
DOI: 10.1070/SM1999v190n11ABEH000437
Sbornik Math. 190 (1999), N11, 1559-1570
Description: Identities of an algebra with a group action and its subalgebra of skew-symmetric elements.

Finite dimensional graded simple algebras
arXiv:math.RA/0512202
Abstract: Let $R$ be a finite-dimensional algebra over an algebraically closed field $F$ graded by an arbitrary group $G$. We prove that $R$ is a graded division algebra if and only if it is isomorphic to a twisted group algebra of some finite subgroup of $G$. If the characteristic of $F$ is zero or ${\rm char} F$ does not divide the order of any finite subgroup of $G$ then we prove that $R$ is graded simple if and only if it is a matrix algebra over a finite-dimensional graded division algebra.

Bahturin, Yuri and Shestakov, Ivan

Gradings of simple Jordan algebras and their relation to the gradings of simple associative algebras
Comm. Alg. 29 (2001), N9, 4095-4102
Zentralblatt: 1054.17025
Availability: 100105990.pdf

Bahturin, Y.A. and Shestakov, I.P. and Zaicev, M.V.

Gradings on simple Jordan and Lie algebras
DOI: 10.1016/j.jalgebra.2004.10.007
J. Algebra 283 (2005), N2, 849-868
Description: Description of all gradings by finite abelian groups of several types of classical Lie algebras, p=0. This paper is (partially) corrected in Bahturin & Zaicev, Involutions on graded matrix algebras, J. Algebra 315 (2007), No.2, 527-540 [Zbl 1129.16033].
Availability: hardcopy

Bahturin, Yu.A. and Slinko, A.M. and Shestakov, I.P.

Non-associative rings
DOI: 10.1007/BF01255614
Algebra. Topologiya. Geometriya, Vol. 18, VINITI, 1981, 3-
J. Sov. Math. 18 (1982), 169-211
Zentralblatt: 486.17001
Description: A VINITI survey for 1972-1978, including some aspects of Lie algebras.
Availability: algebra-top-geom-18.djvu (whole book); hardcopy

Bahturin, Yu. A. and Strade, H.

Some examples of locally finite simple Lie algebras
Arch. Math. 65 (1995), No.1, 23-26
Zentralblatt: 0823.17007
Description: Families of locally finite dimensional simple Lie algebras are constructed, which can not be presented as direct limits of finite dimensional simple Lie algebras. This answers a question raised in Amayo-Stewart book.

Locally finite-dimensional simple Lie algebras
DOI: 10.1070/SM1995v081n01ABEH003618
Sbornik Math. 81 (1995), no.1, 137-161
MR 95a:17025
Zentralblatt: 0829.17016
Description: An example of uncountably many pairwise nonisomorphic locally finite-dimensional simple Lie algebras, each being a direct limit of the family sl(n). A locally finite-dimensional simple Lie algebra over an algebraically closed field of characteristic p>7 satisfies a polynomial identity if and only if the dimensions of the classical simple factors are bounded.
Availability: bah18502.ps; hardcopy

Bahturin, Yuri and Tvalavadze, Marina

Group gradings on G_2
arXiv:math.RA/0703468

Bahturin, Y. and Tvalavadze, M. and Tvalavadze, T.

Sums of simple and nilpotent Lie algebras
DOI: 10.1081/AGB-120013332
Comm. Algebra 30 (2002), N9, 4455-4471
Zentralblatt: 1026.17011
Abstract: We present some results about Lie algebras, which can be written as the sum of two subalgebras in two cases: where both subalgebras are simple or both are nilpotent. In the first case we suggest new examples of simple Lie algebras admitting decomposition into the sum of simple subalgebras and give explicit realizations where the existence of such decompositions was established earlier. We single out cases where such decomposition is not possible. We also construct examples of solvable Lie algebras, which are the sums of two nilpotent subalgebras, and the derived length of the sum is greater than the sum of the nilpotent indexes of the summands.
Availability: hardcopy

Bahturin, Y.A. and Zaicev, M.V.

Identities of graded algebras
DOI: 10.1006/jabr.1997.7017
J. Algebra 205 (1998), no.1, 1-12
MR 99f:17034
Zentralblatt: 0920.16011
Description: Notion of algebras of Lie type, namely, a(bc)=alpha(ab)c + beta(ac)b for some scalars alpha, beta for every a,b,c, generalizing notion of associative and Lie superalgebras.
Availability: 1998-identities.pdf

Group gradings on matrix algebras
Canad. Math. Bull. 45 (2002), No.4, 499-508

Graded algebras and graded identities
Polynomial Identities and Combinatorial Methods (ed. A. Giambruno, A. Regev, M. Zaicev), Lect. Notes Pure Appl. Math. 235, M.Dekker, 2003, 101-
Description: A survey on gradings in associative algebras.
Availability: 2003-polynomial-identities-and-combinatorial-methods.djvu (whole book)
google books

Group gradings on simple Lie algebras of type "A"
J. Lie Theory 16 (2006), No. 4, 719--742
arXiv:math.RA/0506055
Zentralblatt: 1141.17006

Bai, Chengming

A unified algebraic approach to classical Yang-Baxter equation
DOI: 10.1088/1751-8113/40/36/007
J. Phys. A: Math. Theor. 40 (2007), 11073-11082
arXiv:0707.4226

Bijective 1-cocycles and classification of 3-dimensional left-symmetric algebras
arXiv:0710.2609

Left-symmetric bialgebras and analogue of the classical Yang-Baxter equation
DOI: 10.1142/S0219199708002752
Comm. Contemp. Math. 10 (2008), N2, 221-260
Abstract: ... a left-symmetric bialgebra is equivalent to a symplectic Lie algebra with a decomposition into a direct sum of the underlying vector spaces of two Lagrangian subalgebras.

Double constructions of Frobenius algebras and nondegenerate Connes 2-cocycles and their duality
arXiv:0808.3330
Description: Inavraint bilinear form and Lie-like 2-cocycles on associative algebras.

Bai, Chengming and Meng, Daoji (=Meng, Dao Ji)

The structures of bi-symmetric algebras and their sub-adjacent Lie algebras
DOI: 10.1080/00927870008826988
Commun. Algebra 28, No.6, 2717-2734 (2000)
Zentralblatt: 0966.17001
Availability: 2000-structures.pdf

The classification of Novikov algebras in low dimensions: invariant bilinear forms
J. Phys. A 34 (2001), no.8, 1581-1594; Addendum: 34 (2001), no.39, 8193-8197
MR 2002d:17002

Left-symmetric algebras and complete Lie algebras
DOI: 10.1081/AGB-120013195
Comm. Alg. 30 (2002), N2, 1001-1015

On the Novikov algebra structures adapted to the automorphism structure of a Lie group
DOI: 10.1016/S0393-0440(02)00127-4
J. Geom. Phys. 45 (2003), N1-2, 105-115
Description: Including a survey on Novikov algebras
Availability: novikov-algebra.pdf

A Lie algebraic approach to Novikov algebras
DOI: 10.1016/S0393-0440(02)00150-X
J. Geom. Phys. 45 (2003), N1-2, 218-230
Description: Including some survey. Construction of Novikov algebras from Lie algebars by taking x*y = [f(x),y]. Deformations. Examples in low dimension.
Availability: lie-algebraic.pdf

Bai, Chengming and Meng, Daoji and He, Sui

Derivations on Novikov Algebras
DOI: 10.1023/A:1024437815600
International Journal of Theoretical Physics Volume 42, Number 3 / March, 2003 Pages 507-521
Description: Not very deep. Many examples in low dimensions.

Bai, Chengming and Meng, Daoji and Zhang, Hong-Biao

On the central extensions of Poisson brackets of hydrodynamic type
J. Phys. A 36 (2003), no. 9, 2261--2269

Bai, Z. D. and Silverstein, J. W. and Yin, Y. Q.

A note on the largest eigenvalue of a large dimensional sample covariance matrix
J. Mult. Anal. 26:166 168 (1988)

Bailey, R.A. and Gower, J.C.

Approximating a symmetric matrix
DOI: 10.1007/BF02294615
Psychometrika 55 (1990), N4, 665-675
Description: Least-square approximation (from a statistical viewpoint) to a symmetric matrix.
Availability: 1990-approximating.pdf

Bajo, Ignacio and Benayadi, Said

Lie algebras admitting a unique quadratic structure
DOI: 10.1080/00927879708826023
Comm. Algebra 25 (1997), N9, 2795-2805
Description: Over p=0, a Lie algebra admitting uinque, up to scalar, symmetric bilinear invariant nondegenerate form, is simple.
Availability: 780053603.pdf

Lie algebras with quadratic dimension equal to 2
DOI: 10.1016/j.jpaa.2006.07.010
J. Pure Appl. Alg. 209 (2007), N3, 725-737
Description: Lie algebras equipped with a nonsingular symmetric bilinear invariant form.
Availability: 2007-lie.pdf

Bajo, I. and Benayadi, S. and Bordemann, M.

Generalized double extension and descriptions of quadratic Lie superalgebras
arXiv:0712.0228
Description: Lie superalgebras with supersymmetric, even, non-degenerate invariant bilinear form.

Bajo, I. and Benayadi, S. and Medina, A.

Symplectic structures on quadratic Lie algebras
DOI: 10.1016/j.jalgebra.2007.06.001
arXiv:math.RA/0603066
J. Algebra 316 (2007), N1, 174-188
Description: Symplectic Lie algebras are Lie algebras with nondegenerate 2-cocycle. Quadratic Lie algebras are Lie algebras with nondegenarte invariant symmetric form. Lie algebras which are simultaneously symplectic and quadratic.

Bajorska, B. and Macedonska, O.

On the Boffa alternative
URL: http://journals.impan.gov.pl/cm/Inf/88-2-7.html http://mat.polsl.pl/pracownicy/olga/pliki/0-Boffa.ps
Colloq. Math. 88 (2001), No.2, 257-261
Zentralblatt: 0986.20031
Availability: 0-Boffa.ps

On positive law problems in the class of locally graded groups
URL: http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=13304204&site=ehost-live http://mat.polsl.pl/pracownicy/olga/pliki/olga-pub.html
Comm. Algebra 32 (2004), No.5, 1841-1846
Zentralblatt: 1069.20016
Description: Some particular answer to Boffa's question.
Availability: 13304204.pdf

Bakalov, Bojko

Vertex (Lie) algebras in higher dimensions
math-ph/0608054
Description: A survey?

Bakalov, Bojko and D'Andrea, Alessandro and Kac, Victor G.

Theory of finite pseudoalgebras
math.QA/0007121
Adv. Math. 162 (2001) 1-140

Bakalov, Bojko and Kac, Victor G.

Field algebras
Int. Math. Res. Not. 3(2003), 123-159
Abstract: A field algebra is a noncommutative generalization of a vertex algebra. In this paper, we develop foundations of the theory of field algebras.

Bakalov, Bojko and Kac, Victor G. and Voronov, Alexander A.

Cohomology of conformal algebras
Comm. Math. Phys. 200(1999), 561-598
math.QA/9803022
Description: Theory of Lie-like algebras over C[d] with some parameter \lambda in Jacobi identities: examples (analogues of Virasoro, current algebras) and cohomology theory. Relates to works of Gelfand, Fuchs and Feigin, relations with conformal analogues of Hochschild and cyclic cohomology. Doesn't touch general case like L \tensor A.

Baker, Andrew

Matrix Groups. An Introduction to Lie Group Theory
DOI: 10.2307/3647845
Springer, 2002
Review: Amer. Math. Monthly 110 (2003), No.5, 446-455 (very critical)
Description: Examples of Lie groups which are not matrix groups.
Availability: Kolkhoz; 2002-matrix-groups.djvu

a
m
a
z
o
n

Baker, G. A.

Populations with means and standard deviations of samples independently distributed
DOI: 10.2307/2307577
Amer. Math. Monthly 60 (1953), No.3, 182-183
Availability: 1953-populations.pdf

Bakiev, M.N and Dzhumadildaev, A.S

The kernel space of a Witt algebra
Russ. Math. Surv. 43, No.4, 203-204 (1988)
Zentralblatt: 0658.17012
Description: interpretation of H^3 as "kernels"
Availability: hardcopy

Bakirova, Margarita and Dorodnitsyn, Vladimir and Kozlov, Roman

Symmetry-preserving discrete schemes for some heat transfer equations
math.NA/0402367
Abstract: Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant difference equations and meshes, where the original continuous symmetries are preserved in discrete models. Conservation of symmetries in difference modeling helps to retain qualitative properties of the differential equations in their difference counterparts.

Balaba, I. N. and Pikhtilkov, S. A.

A prime radical of special Lie superalgebras
Proceedings of the International Session of the Algebraic Seminar dedicated to the 70th Anniversary of the Algebraic Seminars of Moscow State University. Fundam. Prikl. Mat. 9 (2003), no. 1, 51-60

Balashchenko, V.V.

Invariant f-structures on naturally reductive homogeneous spaces
DOI: 10.3103/S1066369X08040014
Russian Mathematics (Izv. VUZ) 52 (2008), N4, 1-12
Availability: 2008-invariant.pdf

Balavoine, David

Deformations des algebres de Leibniz
CRAS 319 (1994), 783-788
Description: Standard deformation theory for Leibniz algebras is outlined (infinitesimal deforms are H^2, obstructions are H^3, etc.)
Availability: hardcopy

Deformations et rigidite geometrique des algebres de Leibniz
DOI: 10.1080/00927879608825618
Comm. Algebra 24 (1996), N3, 1017-1034

Deformations of algebras over a quadratic operads
Operads: Proc. Renaissance Conf, Contemp. Math. 202(199?), 207-234
Description: General deform. theory including Koszul duality and operads. Super-Lie structure on H^*(A,A) for associative, Lie and commutative A from operadic unifying point of view.
Availability: hardcopy (book)

Homology and cohomology with coefficients, of an algebra over a quadratic operad
DOI: 10.1016/S0022-4049(97)00131-X
J. Pure Appl. Algebra 132 (1998), No.3, 221-258
Zentralblatt: 0967.18004
Availability: science.pdf; hardcopy

Baldwin, J, and Berman, J.

The number of subdirectly irreducible algebras in a variety
Algebra Universalis 5 (1975), 379-389.

Baldwin, John T. and Rose, Bruce

$\aleph_0$-categoricity and stability of rings
J. Algebra 45, 1-16 (1977)
Zentralblatt: 0368.16001

Balinsky, A.A. and Burman, Yu.M.

Quadratic Poisson brackets compatible with an algebra structure
DOI: 10.1088/0305-4470/27/18/008
J. Phys. A Math. Gen. 27 (1994), No.18, L693-L696
Zentralblatt: 0844.58024
Zbl Review: Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.
Availability: ja941808.pdf

Balinsky, A.A. (=Balinskij, Balinskii) and Novikov, S.P.

Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras
Sov. Math. Dokl. 32 (1985), N1, 228-231
Dokl. Akad. Nauk SSSR 283 (1985), N5, 1036-1039
MR 87h:58057
Zentralblatt: 0606.58018
Zbl Review: Poisson brackets on function spaces specified by formulae of the form $$ \{u\sp i(x),u\sp j(x)\}=g\sp{ij}(u(x)\delta '(x-y)+u\sp k\sb x b\sb k\sp{ij}(u(x))\delta (x-y) $$ are studied. In particular the case when $g\sp{ij}$ is linear in u and $b\sb k\sp{ij}$ are constant is considered. The properties of such a bracket are related to the properties of the finite dimensional algebra with structure constants $b\sb k\sp{ij}$.
Description: This is apparently what led further to "Novikov algebras"

Ballester-Bolinches, A. and Esteban-Romero, R. and Robinson, Derek J. S.

On finite minimal non-nilpotent groups
Proc. Amer. Math. Soc. 133 (2005), 3455-3462

Ballester-Bolinches, Adolfo and Ezquerro, Luis M.

Classes of finite groups
DOI: 10.1007/1-4020-4719-3
Springer, 2006, 385 p.
Description: Survey of what is known about classificaltion of solvable and generally (non-simple) finite groups.

Ballesteros, Angel and Celeghini, E. and del Olmo, M.A.

The Drinfeld double gl(n) \oplus t_n
J. Phys. A 39 (2006), no. 29, 9161--9168

Classical Lie algebras and Drinfeld doubles
DOI: 10.1088/1751-8113/40/9/007
J. Phys. A: Math. Theor. 40 (2007), 2013-2022
arXiv:math.GR/0611393
Abstract: The Drinfeld double structure underlying the Cartan series An, Bn, Cn, Dn of simple Lie algebras is discussed. This structure is determined by two disjoint solvable subalgebras matched by a pairing. For the two nilpotent positive and negative root subalgebras the pairing is natural and in the Cartan subalgebra is defined with the help of a central extension of the algebra. A new completely determined basis is found from the compatibility conditions in the double and a different perspective for quantization is presented. Other related Drinfeld doubles on C are also considered.

Simple algebras and Drinfeld doubles
DOI: 10.1134/S1063778808050062
Physics of Atomic Nuclei; May2008, Vol. 71 Issue 5, p807-811

Ballesteros, A. and Gromov, N. A. and Herranz, F. J. and del Olmo, M. A. and Santander, M.

Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras
J.Math.Phys. 36 (1995) 5916-5937
hep-th/9412083, 26 pages
Abstract: Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras $so(p,q)$ starting from the one corresponding to $so(N+1)$. It allows to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for the cases $N=2,3,4$. All Lie bialgebra contractions studied in this paper define Hopf algebra contractions for the Drinfel'd-Jimbo deformations $U_z so(p,q)$. They are explicitly used to generate new non-semisimple quantum algebras as it is the case for the Euclidean, Poincare' and Galilean algebras.

Banaschewski, B.

The Birkhoff Theorem for varieties of finite algebras
DOI: 10.1007/BF01194543
Algebra Universalis Volume 17, Number 1 / December, 1983 Pages 360-368

Bandman, Tatiana and Borovoi, Mikhail and Grunewald, Fritz and Kunyavskii, Boris and Plotkin, Eugene

Engel-like characterization of radicals in finite dimensional Lie algebras and finite groups
DOI: 10.1007/s00229-006-0627-0
arXiv:math.GR/0411463
Manuscr. Math. 119 (2006), N4, 465-481
Description: Over p=0. For p>0, counterexamples are provided.

Bandman, Tatiana and Greuel, Gert-Martin and Grunewald, Fritz and Kunyavskii, Boris and Pfister, Gerhard and Plotkin, Eugene

Engel-like identities characterizing finite solvable groups
Max-Plank-Inst. Math. Bonn preprint 2003
Description: An impressive combination of algebraic geometry, group theory and computer calculations.
Availability: hardcopy

Identities for finite solvable groups and equations in finite simple groups
DOI: 10.1112/S0010437X0500179X
Compositio Mathematica 142 (2006), 734-764
Description: This is probably a published version of the preprint above.

Bando, S. and Siu, Y.-T.

Stable sheaves and Einstein-Hermitian metrics
Preprint, circa 1995-1996, 13 pp.
Availability: hardcopy

Bankston, Paul

A survey of ultraproduct constructions in general topology
Topology Atlas Invited Contributions 8(2003), no. 2, 1-32

Bannai, E. and Ito, T.

Algebraic Combinatorics
(in Russian)
Availability: 1075.djv; amazon

Bar-Natan, Dror and Le, Thang T. Q. and Thurston, Dylan P.

Two applications of elementary knot theory to Lie algebras and Vassiliev invariants
math.QA/0204311
Geom. Topol. 7(2003), 1-31
Description: A new proof of the multiplicativity of the Duflo-Kirillov map S(g) -> U(g) for metrized Lie (super)algebras g.

Barakat, Mohamed and Bremer, Barbara

Higher Extension Modules and the Yoneda Product
arXiv:0802.3179
Description: Ext's and modules extensions.

Barakat, Mohamed and Robertz, Daniel

homalg - a meta-package for homological algebra
DOI: 10.1142/S0219498808002813
math.AC/0701146
Journal of Algebra and Its Applications 2008 Vol: 7 Issue: 3 (June 2008) Page: 299 - 317
Description: Maple.

Barannikov, Sergey and Kontsevich, Maxim

Frobenius manifolds and formality of Lie algebras of polyvector fields
DOI: 10.1155/S1073792898000166
Internat. Math. Res. Notices 1998, no. 4, 201--215
alg-geom/9710032
MR 99b:14009
Description: Deformations.

Baranov, A.A.

Volichenko algebras and nonhomogeneous subalgebras of Lie algebras
DOI: 10.1007/BF02112529
Sib. Math. J. 36 (1995), N5, 859-868
Description: Free Volichenko algebras, identities.
Availability: hardcopy; 1995-volichenko.pdf

Finitary simple Lie algebras
DOI: 10.1006/jabr.1999.7856
J. Algebra 219 (1999), N1, 299-329
Description: Classification; also over algebraically nonclosed fields; division algebras with involutiions are involved. Reasonings about forms of finite-dimensional simple Lie algebras and their imbeddings.
Availability: finprepr.ps

Classification of simple finitary Lie algebras over zero characteristic field
Doklady Nat. Acad. Sci. Belarus 44 (2000), N1, 8-10

Baranov, A.A. and Strade, H.

Finitary Lie algebras
J. Algebra 254(2002), N1, 173-211
Zentralblatt: pre01867975
Description: An algebra is called finitary if it consists of finite-rank transformations of a vector space. We classify finitary simple and finitary irreducible Lie algebras over an algebraically closed field of characteristic p ne 2,3.
Availability: FinitaryLieAlgebras.ps

Baranov, A.A. and Zalesskii, A.E.

Quasiclassical Lie algebras
DOI: 10.1006/jabr.2001.8859
J. Algebra 243 (2001), No.1, 264-293
Zentralblatt: 1017.16026
Description: Lie algebras obtained from associative algebras with involution.

Plain representatrions of Lie algebras
JLMS 63(2001), 571-591
Zentralblatt: 1031.17002
Description: p=0, finite-dimensional. A class of representations is studied which "behave well" on Levi subalgebras (in the Levi-Malcev decomposition). Also the theme of relationship between associative algebra A and Lie alebra [A,A] (after Herstein et al.) is touched.
Availability: baranov-zalesskii.pdf

Baranovskii, S. P. and Shirokov, I. V.

Prolongations of Vector Fields on Lie Groups and Homogeneous Spaces
Theoretical and Mathematical Physics 135 (1): 510-519, April 2003
Abstract: We introduce the notion of the \goth{gl}(V)-prolongation of Lie algebras of differential operators on homogeneous spaces. The \goth{gl}(V)-prolongations are topological invariants that coincide with one-dimensional cohomologies of the corresponding Lie algebras in the case where V is a homogeneous space. We apply the obtained results to the spaces S1 (the Virasoro algebra) and \mathbb{R}^1.

Baranovskii, S.P. and Shirokov, I.V. and Shmakov, S.V.

Vychislenie gruppy avtomorfizmov konechnomernoi algebry v sisteme Maple
Mat. Struktury i Modelirovanie 12 (2003)

Barbaumov, V. E.

Algebras, all of whose subalgebras are PI-algebras
DOI: 10.1007/BF00970298
Siberian Math. J. 11 (1970), N6, 1022-1025
Availability: 1970-algebras.pdf; hardcopy

Barberis, María Laura

Abelian hypercomplex structures on central extensions of H-type Lie algebras
Journal of Pure and Applied Algebra, Vol. 158 (1) (2001) pp. 15-23
Description: A characterization of the two-step nilpotent Lie algebras carrying abelian hypercomplex structures.

Barberis, M. L. and Dotti, I.

Abelian complex structures on solvable Lie algebras
J. Lie Theory 14(2004), No.1, 25-34
Description: Abelian complex structure is a mapping J:L->L satisfying J^2 = -1, [Jx,Jy] = [x,y] (earlier it was proved that a Lie algebra admitting such a strcuture is necessary solvable).

Barbour, J.M.

Music and ternary continued fractions
Amer. Math. Monthly 55(1948), 545-555
Availability: music.pdf

Barcelo, Helen and Ram, Arun

Combinatorial representation theory
New perspectives in geometric combinatorics, MSRI Publ. 38(1999), 23-90
Description: a very lovely survey of representation theory of symmetric and linear groups, classical Lie algebras and some generalizations.
Availability: MSRI site

Barcelo, H. and Sundaram, S.

On Some Submodules of the Action of the Symmetrical Group on the Free Lie Algebra
Journal of Algebra Vol. 154, No. 1, January 1, 1993 pp. 12-26

Bardakov, V. G.

Computation of commutator length in free groups.
Algebra and Logic 39 (2000), no. 4, 224--251
MR 2001m:20034

Bardy, Nicole

Definition abstraite de d'un systeme de racines dans le cas symetrisable
J. Alg. 271(2004), 108-178
(Rutwig)
Description: Axiomatics of root systems arising in Kac-Moody.
Availability: Bardy04.pdf

Bardzell, Michael J.

Noncommutative Grobner bases and Hochschild cohomology
Symbolic computation: solving equations in algebra, geometry, and engineering, Contemp. Math. 286 (2001), 227-240

Bardzell, Michael J. and Marcos, Eduardo N.

H^1 and presentations of finite dimensional algebras
Representations of algebras, LN Pure Appl. Math., 224, M. Dekker, 2001, 31-38

Barkovich O.A. and Beniash-Kryvets, V.V.

On the Tits alternative for some generalized triangle groups of type (3,4,2)
Doklady Nat. Acad. Sci. Belarus 47, Number 6; November--December, 2003. pp. 24--27

Barlet-Mathieu, Cecile

Representations des formes d'une algebre de Kac-Moody
J. Lie Theory 13 (2003), no.2, 591-612

Barndorff-Nielsen, Ole E. and Jupp, Peter E.

Statistics, yokes and symplectic geometry
Annales de la faculté des sciences de Toulouse 6 (1997), no. 3, 389-427
Description: Include likelihood and Lie group actions.

Barndorff-Nielsen, Ole E. and Jupp, Peter E. and Kendall, Wilfrid S.

Stochastic calculus, statistical asymptotics, Taylor strings and phyla
Annales de la faculté des sciences de Toulouse 3 (1994), no.1, 5-62
Description: Stochastic calculus, as opposed to the usual calculus, based on the second-order Taylor-like expansion (as opposed to the first order one). "Tensor and differential geometrtic methods in statistics".

Barnea, Yiftach

Generators of simple Lie algebras and the lower rank of some pro-p groups
Comm. Algebra 30 (2002), 1293-1303
Description: Simple classical Lie algebras over p>0 are 2-generated. Lie algebars of the form g\otimes tF[t].

Maximal graded subalgebras of loop toroidal Lie algebras
DOI: 10.1007/s10468-005-3597-0
Algebr. Represent. Theory 8 (2005), no. 2, 165--171

Barnea, Nurit and Ginosar, Yuval

A separable deformation of the quaternion group algebra
DOI: 10.1090/S0002-9939-08-09480-X
arXiv:0704.1556
Proc. Amer. Math. Soc. 136 (2008), 2675-2681
Description: A separable deformation of quaternion group alebra (of dimension 8) over a field of char. 2 is presented, therefore invalidating counterexample of Gerstnhaber-Giaquinto to the Donald-Flanigan conjecture.
Availability: S0002-9939-08-09480-X.pdf (published version)

Barnea, Yiftach and Isaacs, I. M.

Lie algebras with few centralizer dimensions
Journal of Algebra Volume 259, Issue 1, 1 January 2003, Pages 284-299
Abstract: It is known that a finite group with just two different sizes of conjugacy classes must be nilpotent and it has recently been shown that its nilpotence class is at most 3. In this paper we study the analogs of these results for Lie algebras and some related questions.
Description: over C; Zariski-topology arguments (Lemma 3.1)
Availability: science.pdf

Barnea, Y. and Larsen, M.

J. Algebra 271 (2004), N1, 1-10
Description: Density of generators of open subgroups of G(K), where G is a semisimple algebraic group over a local field K of positive characteristic.

Barnea, Yiftach and Passman, Donald S.

Filtrations in semisimple Lie algebras, I
URL: http://math.wisc.edu/~passman/abstracts.html http://www.ams.org/tran/2006-358-05/S0002-9947-05-03986-3/home.html http://personal.rhul.ac.uk/unai/254/
Trans. Amer. Math. Soc. 358 (2006), 1983-2010

Filtrations in semisimple Lie algebras, II
URL: http://math.wisc.edu/~passman/abstracts.html http://personal.rhul.ac.uk/unai/254/
DOI: 10.1090/S0002-9947-07-04224-9
Trans. Amer. Math. Soc. 360 (2008), 801-817

Barnea, Y. and Shalev, A. and Zelmanov, E.

Graded subalgebras of affine Kac-Moody algebras
DOI: 10.1007/BF02897069
Israel J. Math. 104 (1998), 321-334
Zentralblatt: 0930.17022
Description: Loop algebras are involved.
Availability: kacmoody.ps

Barnes, D.W. and Gastineau-Hills, H.M.

On the theory of soluble Lie algebras
URL: http://www.digizeitschriften.de/resolveppn/GDZPPN002403102 http://resolver.sub.uni-goettingen.de/purl?GDZPPN002403102
Math. Z. 106 (1968), 343-354
MR 38:1130
Description: Splitting over minimal ideals etc.
Availability: PPN266833020_0106__0_0.pdf

Barnes, Donald W. and Groves, Daniel

The Wielandt subalgebra of a Lie algebra
J. Aust. Math. Soc. 74(2003), N3, 313-330
MR 2004c:17007 (me)
Availability: hardcopy

Barnes, Donald W. and Lambe, Larry A.

A Fixed Point Approach to Homological Perturbation Theory
Proceedings of the American Mathematical Society, Vol. 112, No. 3 (Jul., 1991), pp. 881-892
MR 91j:55019

Barnes DW and Mack JM.

An Algebraic Introduction to Mathematical Logic
DOI: 10.1090/S0002-9904-1977-14253-5
Springer GTM 22, 1975, 136 pp. (reprinted by Beijing World Publishing Corporation, 1988?)
MR 52:10362
Review: Bull. Amer. Math. Soc. 83 (1977), 186-188
Description: For example, fisrt-order formulas defined as elements of a certain free algebra factored out by (complicated) congruence relation.

Barnes, Donald W. and Newell, Martin L.

Some theorems on saturated homomorphs of soluble Lie algebras
DOI: 10.1007/BF01109856
Math. Z. 115 (1970), N3, 179-187
MR 42:1871
Description: Low-dimensional cohomology via Hochschild-Serre spectral sequence.
Availability: barnes-newell.pdf

Barnes, Donald W.

Nilpotency of Lie algebras
Math. Z. 79 (1962), 237-238
MR 27:180
Description: If each maximal subalgebra of L is an ideal, then L is nilpotent.

Lattice isomorphisms of Lie algebras
Journal of the Australian Mathematical Society, 4 (1964), 470-475
MR 30:3902

On the cohomology of soluble Lie algebras
Math. Z. 101 (1967), 343-349
MR 36#3836
Zentralblatt: 0166.04102
Description: Conditions for the cohomology of a solvable Lie algebra to be trivial. Typical results are: (a) If A is a minimal ideal of a solvable Lie algebra L equal to its centralizer in L, then L splits over A and all complements of A are conjugate under exp(ad_A) (b) L is supersoluble if and only if all of its maximal subalgebras have codimension 1. (c) If L is nilpotent and L^A = 0, then H^n(L,A) = 0.
Availability: hardcopy

On Cartan subalgebras of Lie algebras
DOI: 10.1007/BF01109800
Math. Z. 101 (1967), 350-355
MR 36:3837

Lattice automorphisms of semi simple Lie algebras
J. Austral. Math. Soc. 16 (1973), 43-53
MR 51:626

Sortability of representations of Lie algebras
DOI: 10.1016/0021-8693(73)90059-8
J. Alg. 27 (1973), 486-490
MR 51:3242
Zentralblatt: 0272.17002
Description: Lie algebras with a property that every finite-dimensional indecomposable module contains only one type of composition factor. The technique is a trivial application of Hochschild-Serre spectral sequence and cohomological long exact sequence associated with extension of modules for low-dimensional cohomology.
Availability: 1973-sortability.pdf; hardcopy

The Frattini argument for Lie algebras
DOI: 10.1007/BF01177868
Math. Z. 133 (1973), N4, 277-283
MR 48:8582

First cohomology groups of soluble Lie algebras
DOI: 10.1016/0021-8693(77)90407-0
J. Algebra 46 (1977), no.1, 292-297
MR 56#3078
Description: If p=0 or L is solvable, then H^1(L,M) = 0 iff L has no abelian complemented chief factor isomorphic to M. If p=0, then H^1(L,M)=0 for any irreducible module M of dimension > 1 iff L is a direct sum of semisimple and supersolvable Lie algebras.
Availability: 1977-first.pdf; hardcopy

On F-hypercentral modules for Lie algebras
DOI: 10.1007/BF01226013
Arch. Math. 30 (1978), N1, 1-7
MR 58:22199
Availability: 1978-hypercentral.pdf

Spectral Sequence Constructors in Agebra and Topology
Memoirs AMS, No. 317, 1985; paperback, 174 pp.
MR 86e:55032
Availability: hardcopy (book); google books

Finitely sorting Lie algebras
J. Aust. Math. Soc. Ser. A 49 (1990), No.3, 354-363
Zentralblatt: 0748.17016
Description: Some criteria for vanishing of cohomology.

On the length of the spectral sequence of a Lie algebra extension
Proc. Amer. Math. Soc. 129 (2001), No.2, 347-350
MR 2001i:17025
Zentralblatt: 0972.18009
Availability: S0002-9939-00-05761-0.pdf; hardcopy

On the length of the spectral sequence of a Lie algebra extension, II
DOI: 10.1006/jabr.2000.8533
J. Algebra 234 (2000), N2, 419-422
MR 2001k:17032
Zentralblatt: 0972.18010
Description: Some examples.

On F-hyperexcentric modules for Lie algebras
J. Aust. Math. Soc. 74 (2003), 235-238
MR 2004b:17039
Availability: w72.pdf

Ado-Iwasawa extras
J. Aust. Math. Soc. 78 (2005), 407-421
MR 2142164
Zentralblatt: 1075.17006
Description: Refinement of Ado's theorem (related to supersolubility etc.).
Availability: r76.pdf

Schunck classes of soluble restricted Lie algebras
arXiv:math/0610609

Barnes, Marcus Emmanuel

A loop module of the extended affine algebra of type A
New Zealand J. Math. 33 (2004), no. 1, 11--15
Availability: MEB.pdf (Preprint, August 2002)

Barnes, Richard T.

On splitting fields for certain Lie algebras of prime characteristic
PAMS 17(1966), 930-935
Description: Every Lie algebra of classical type has a separable splitting field.

Barou, G. and Malliavin, M.-P.

Sur la resolution injective minimale de l'algebre enveloppante d'une algebre de Lie resoluble
JPAA 37(1985), 1-25
Availability: hardcopy

Barr, Michael

A cohomology theory for commutative algebras. I, II
PAMS 16 (1965), 1379-1391
Availability: pams-[12].pdf

A note on commutative algebra cohomology
BAMS 74 (1968), 310-313
Description: The commutative algebra cohomology theory defined by Gerstenhaber, does not in general vanish in degree 3 even if the module is injective, hence the theory cannot be described as the derived functor of the second cohomology group. Every element of the third cohomology group can be regarded as obstruction in the sense of Harrison.
Availability: hardcopy

Harrison cohomology, Hochschild cohomology and triples
DOI: 10.1016/0021-8693(68)90062-8
J. Alg. 8 (1968), 314-323
Description: Harrison cohomology coincides with symmetric triple cohomology in characteristic 0.
Availability: science.pdf

Cartan-Eilenberg cohomology and triples
JPAA 112 (1996), 219-238
Description: Comparison of Cartan-Eilenberg and Beck approaches to cohomology of Lie algebras.

Acyclic Models
URL: http://www.crm.umontreal.ca/fr/niveau2/index_pub.html http://www.ams.org/bookstore-getitem/isbn=0-8218-2877-0
AMS, 2002, 179pp.
Abstract: The book contains an introduction to categories (largely cribbed from TTT) and abelian categories, then on to chain complexes and triples before stating the main theorem whose proof is essentially trivial since I discovered the way of doing it with categories of fractions. Then come applications in algebra and topology.
Availability: 39$ ($18 sale)

A duality on simplicial complexes
Georgian Math. J. 9 (2002), No. 4, 601-605
Description: Duality between homology and cohomology of simplicial complexes.

Algebraic cohomology: The early days
Galois Theory, Hopf Algebras, and Semiabelian Categories (ed. G.Janelidze, B.Pareigis and W.Tholen), AMS, 2004
google books

Preserving homology
Theor. Appl. Categ. 16 (2006), No. 7, 132-143
Description: What it means for a functor to preserve homology?

Barr, Michael and Beck, John

Homology and standard constructions
Seminar on Triples and Category Theory, Reprints in Theory and Appl. of Categories, 2008, N18, 185-
LNM 80
Description: Including Mayer-Vietoris long exact sequence.

Barr, M. and Rinehart

Cohomology as the derived functor of derivations
DOI: 10.2307/1994557
TAMS 122(1966), 416-426

Bars, I. and Morel, B. and Ruegg, H.

Kac-Dynkin diagrams and supertableaux
J. Math. Phys. 24(1983), N9, 2253-2262
Abstract: We show the relation between Kac-Dynkin diagrams and supertableaux.

Bartholdi, Laurent

Lie algebras and growth of branch groups
Pacific J. M. 218 (2005), N2, 241-
arXiv:math/0101222
Description: To N-graded Lie algebra, a graph is associated.
Availability: hardcopy (journal)

On amenability of group algebras, II: graded algebras
arXiv:math/0611709
Description: Some curious Hecke-like "deformations" of group algebras.

Bartholdi, Laurent and Enriquez, Benjamin and Etingof, Pavel and Rains, Eric

Groups and Lie algebras corresponding to the Yang-Baxter equations
DOI: 10.1016/j.jalgebra.2005.12.006
J. Algebra 305 (2006), N2, 742-764
Description: Cohomology of some Lie algebras associated to QYBE. Malcev correspondence between these Lie algebras and appropriate groups.

Bartholdi, Laurent and Grogorchuk, Rostislav I.

Lie methods in growth of groups of finite width
math.GR/0002010
Description: A notion of Cayley graph of N-graded Lie algebra.

Bartholdi, Laurent and Grigorchuk, Rostislav I. and Sunik, Zoran

Branch groups
Handbook of Algebra, Vol. 3, 989--1112, North-Holland
arXiv:math.GR/0510294
Description: A survey; branch groups are groups with some fine normal subgroup structure; relations to just-finite, free groups, etc.
Availability: vol3.djvu (whole book)

Bartholdi, Laurent and Liardet, Fabrice

Theorie des groupes et psychologie de l'intelligence
math.HO/0505651
Abstract: We describe the links between group theory and psychology, in particular through the works of Piaget. We show that groups appear universally in his description of children's intelligence, and that the notion of groupoid, which was little considered in psychology, may be fundamental.

Barton, C.H. and Sudbery, A.

Magic squares and matrix models of Lie algebras
math.RA/0203010
Adv. Math. 180(2003), no. 2, 596-647
Description: Exceptional Lie algbras, KKT construction, nmonassociative division algebras and such.

Barut, A.O. and Raczka, R.

Theory of Group Representations and Applications
URL: http://www.krelib.com/matematika/557 http://www.krelib.com/matematika/558 http://techlibrary.ru/books.htm http://www.newlibrary.ru/book/barut_a__ronchka_r/teorija_predstavlenija_grupp_i_ee_prilozhenija_tom1.html http://www.newlibrary.ru/book/barut_a__ronchka_r/teorija_predstavlenija_grupp_i_ee_prilozhenija_tom2.html http://lib.prometey.org/?id=14681&page=1 http://lib.prometey.org/?id=14682&page=1
Einstein, Bishkek, 1997 (reprint of Mir, 1980 - Russian translation from PWN - Polish Sci. Publ., Warszawa, 1977); paperback, 455 + 395 pp.
Description: Vol. 2: projective representations.
Availability: hardcopy (book); Kolkhoz

a
m
a
z
o
n

o
z
o
n

Basdouri, Imed and Ben Ammar, Mabrouk and Ben Fraj, Nizar and Boujelbene, Maha and Kammoun, Kaouthar and Basdouri, Imed and Ben Ammar, Mabrouk and Dali, B\'echir and Omri, Salem and Basdouri, Imed and Ben Ammar, Mabrouk

Cohomology of the Lie superalgebra of contact vector fields on R^{1|1} and deformations of the superspace of symbols
arXiv:math.RT/0702645

Deformation of Vect(R)-modules of symbols
arXiv:math.RT/0702664
Description: Tensor densities.

Cohomology of $\mathfrak {osp}(1|2)$ acting on linear differential operators on the supercircle $S^{1|1}
arXiv:0709.1768
Description: First cohomology.

Bashford, J.D. and Jarvis, P.D.

The genetic code as a periodic table: algebraic aspects
arXiv:physics/0001066
Availability: hardcopy

A base pairing model of duplex formation. I: Watson-Crick pairing geometries
arXiv:q-bio.BM/0507041
Availability: hardcopy

Bashford, J.D. and Tsohantjis, I. and Jarvis, P.D.

Codon and nucleotide assignments in a supersymmetric model of the genetic code
Preprint UTAS-PHYS-96-45, 1996
Description: Evolution of genetic code modelled after Lie superalgebra sl(6|1).
Availability: hardcopy

A supersymmetric model for the evolution of the genetic code
Proc. Nat. Acad. Sci. USA 95(1998), N3, 987-995
Description: An evolution of genetic code modelled by 64-dimensional representations in the space of codons of Lie superalgebra sl(6|1) (branching rules).
Availability: hardcopy

Bashkirov, Evgenii L.

Transvection parameter sets in linear groups over associative division rings and special Jordan algebras defined by these rings
DOI: 10.1007/s00013-005-1732-0
Arch. Math. 87 (2006), N4, 295-302
Abstract: In this paper we construct a correspondence between a class of irreducible linear groups of finite degree over an associative division ring D and special Jordan rings which are defined by D.

Matrix Lie rings that contain a one-dimensional Lie algebra of semi-simple matrices
J. Prime Res. Math. 3 (2007), 111--119

Basili, Roberta

Resolutions of singularities of varieties of Lie algebras of dimension 3 and 4
J. Lie Theory 12 (2002), No.2, 397-407

Bass, Hyman

Algebraic K-Theory
W.A.Benjamin, 1968
Availability: hardcopy (photocopy of table of contents, preface, chapters 7 and 12, bibliography and index); Kolkhoz; absent on amazon and ozon

Euler characteristics and characters of discrete groups
Inv. Math. 35 (1976), 155-196

Bastin, T. and Kilmister, C.W.

Combinatorial Physics
World Scientific, 1995; hardcover with dustjacket, 178 pp.
Availability: hardcopy (book)

Basu, Saugata

Efficient algorithm for computing the Euler-Poincar\'e characteristic of a semi-algebraic set defined by few quadratic inequalities
arXiv:cs.SC/0605082, 17 pages
accepted for publication in Computational Complexity

Computing the Top Betti Numbers of Semialgebraic Sets Defined by Quadratic Inequalities in Polynomial Time
DOI: 10.1007/s10208-005-0208-8
Foundations of Computational Mathematics Volume 8, Number 1 / February, 2008 Pages 45-80; Erratum Pages 81-95

Basu, Saugata and Pollack, Richard and Roy, Marie-Françoise

Computing the First Betti Number of a Semi-Algebraic Set
DOI: 10.1007/s10208-007-9001-1
Foundations of Computational Mathematics Volume 8, Number 1 / February, 2008 Pages 97-136

Batalin, Igor and Marnelius, Robert

Quantum antibrackets
Goteborg ITP 98-04
Description: Some physical-style reasonings about "quantization of Poisson brackets". What is interesting, expressions xQy - yQx are considered, which seems to be close to a Lie algebra of "rectangular matrices".
Availability: bat-tyutin.{tex,dvi}

Batalin, I.A. and Tyutin, I.V.

General local solution to the cyclic Jacobi equation
Preprint
Description: probably this is the paper Leites-Shch refer to saying there described deformations of Poisson algebra, but the authors had difficulty to publish it.
Availability: tyutin.{tex,dvi}

Bateman, P.T.

On the representation of a number as a sum of three squares
Trans. Amer. Math. Soc. 71 (1951), 70-101
Availability: 10.pdf

Batra, Punita

Oscillator representations of Virasoro algebra
Comm. Algebra 30 (2002), no. 4, 1903--1919.

Representations of twisted multi-loop Lie algebras
J. Algebra 272(2004), no. 1, 404-416

Batten, Peggy and Moneyhun, Kay and Stitzinger, Ernest

On characterizing nilpotent Lie algebras by their multipliers
DOI: 10.1080/00927879608825817
Comm. Algebra 24 (1996), No.14, 4319-4330
Zentralblatt: 0893.17008

Batten, Peggy and Stitzinger, Ernest

Covers of Lie algebras
Comm. Alg. 24 (1996), 4301-4317
Zentralblatt: 0893.17004

Baudisch, Andreas

Decidability and stability of free nilpotent Lie algebras and free nilpotent p-groups of finite exponent
Ann. Math. Logic 23 (1982), 1-25
Availability: science.pdf

On elementary properties of free Lie algebras
Proc. ICM-82, 1983, Sect. I, p.4

Tensor product of modules and elementary equivalence
DOI: 10.1007/BF01191499
Algebra Universalis 19 (1984), 120-127
Availability: q273155185214311.pdf

On elementary properties of free Lie algebras
Ann. Pure Appl. Logic 30 (1986), 121-136
Availability: hardcopy

Bauer, Ingrid and Catanese, Fabrizio and Grunewald, Fritz

Beauville surfaces without real structures. I
Preprint, August 2, 2004
Availability: hardcopy

Baues, H.-J. and Jibladze, M. and Pirashvili, T.

Third Mac Lane cohomology
DOI: 10.1017/S030500410700076X
arXiv:math.KT/0604447
Mathematical Proceedings of the Cambridge Philosophical Society (2008), 144: 337-367 Cambridge University Press
Abstract: Based on the computation of the third author we obtain an interpretation of the third Mac Lane cohomology of rings using certain kind of crossed extensions of rings in the quadratic world.

Baues, Hans-Joachim and Minian, Elias Gabriel

Crossed extensions of algebras and Hochschild cohomology
Homology, Homotopy and Applications 4 (2002), 63-82
Abstract: We introduce the notion of crossed n-fold extensions of an algebra B by a bimodule M and prove that such extensions represent classes in the Hochschild cohomology of B with coefficients in M. Moreover we consider this way characteristic classes of chain (resp. cochain) algebras in Hochschild cohomology.

Baues, Hans-Joachim and Minian, Elias Gabriel and Richter, Birgit

Crossed modules over operads and operadic cohomology
DOI: 10.1023/B:KTHE.0000021399.05635.63
K-Theory 31 (2004), N1, 39-69
Abstract: It is known that elements in the cohomology of groups and in the Hochschild cohomology of algebras are represented by crossed extensions. We introduce the notion of crossed modules and crossed extensions for algebras over operads and obtain in this way an operadic version of Hochschild cohomology.

Baues, H.J. and Pirashvili, T.

The universal coefficient theorem for quadratic functors
Preprint MPI fuer Mathematik, Bonn, 1995
J. Pure Appl. Algebra, to appear
Description: Computations of homology groups in variety of groups defined by Leedham-Green.

Shukla cohomology and additive track theories
arXiv:math.KT/0401158
Description: Comparison of Shukla and Hochschild cohomology, including low-dimensional interpretations. Seems to be mostly expository.

Baues, Hans-Joachim

Combinatorial foundation of homology and homotopy applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions
Springer, 1999
Availability: 50 EUR (springer sale)

Track extensions of categories and cohomology
K-Theory 23 (2001), 1-13
Description: Cohomology of a category.

Oliver Baues

URL: http://links.jstor.org/sici?sici=0002-9947(199907)351%3A7%3C2979%3ALAF%3E2.0.CO%3B2-0
TAMS 351 (1999), No.7, 2979-2996
Description: Classification of left-symmetric algebras whose commutaion Lie algebra is gl(n).
Availability: 1999-left.pdf

Baum, Paul and Connes, Alain

Leafwise homotopy equivalence and rational Pontrjagin classes
Preprint IHES, 1983
Availability: hardcopy

Baumann, G.

Symmetry Analysis of Differential Equations Using MATHLIE
Journal of Mathematical Sciences 108 (6): 1052-1069, March 2002

Baumslag, Gilbert and Fine, Benjamin and Xu, Xiaowei

Cryptosystems using linear groups
Appl. Algebra Eng. Comm. Comp. 17 (2006), N3-4, 205-217

Baumslag, G. and Miller, C.F. III and Short, H.

Isoperimetric inequalities and the homology of groups
Description: Linked second homology of a group and its isoperimetric properties (words length).
Availability: bms1-approx-euler.pdf

Baumslag, Gilbert and Myasnikov, Alexei and Remeslennikov, Vladimir

Algebraic geometry over groups. I. Algebraic sets and ideal theory
J. Algebra 219 (1999), 16-79
Description: Linear groups over commutative ring are equationally noetherian, i.e. every system of equations over group has solutions iff any its finite subsystem has solutions.
Availability: alggeom1.pdf

Baur, Walter and Cherlin, Gregory and Macintyre, Angus

Totally categorical groups and rings
DOI: 10.1016/0021-8693(79)90230-8
Journal of Algebra Volume 57, Issue 2, April 1979, Pages 407-440
Description: Also extensive survey of previous results.
Availability: 1979-totally.pdf

Baur, H. and Stammbach, U.

A note on parafree Lie algebras
DOI: 10.1080/00927878008822501
Comm. Algebra 8 (1980), N10, 953-960
Description: Lie algebras whose central series coincides with those of a free Lie algebra.
Availability: 780076768_content.pdf

Baur, Karin and Wallach, Nolan

A class of gradings of simple Lie algebras
Lie algebras, vertex operator algebras and their applications, 3--15, Contemp. Math. 442 (2007)

Bautista, Cesar

A Poincare--Birkhoff--Witt theorem for generalized Lie color algebras
DOI: 10.1063/1.532471
J. Math. Phys. 39 (1998), N7, 3828-

Bautista, Raymundo and Yingbo, Zhang

Representations of a k-algebra over the rational functions over k
J. Algebra 267 (2003), N1, 342-358
Description: Relations between representations of associative algebra G and G\otimes K((x)).

Bauval, A.

Une condition necessaire d'equivalence elementaire entre anneaux de polynomes sur des corps
CRAS 295 (1982), N2, 31-33
Description: When F[X] is elementary equivalent to F'[Y].
Availability: Central Icelandic library, 3rd floor

Bavula, Vladimir

Classification of simple sl(2)-modules and finite-dimensionality of the module of extensions of simple sl(2)-modules
DOI: 10.1007/BF01056594
Ukr. Math. J. 42 (1990), No.9, 1044-1049
Zentralblatt: 0717.17008
Description: New classification of infinite-dimenional sl(2)-moules over p=0 (alternative to those of Block) and Ext^1 between them.
Availability: hardcopy

Computation of H^*(sl(2),M) with coefficients in a simple sl(2)-module
Funct. Anal. Prilozh. 26 (1992), No.1, 57-58
MR 93f:17033 (me)
Availability: hardcopy

Generalized Weyl algebras, kernel and tensor-simple algebras, their simple modules
Proceedings of the sixth international conference on representations of algebras, held at the Carleton University (ed. V. Dlab et al.), Carleton-Ottawa Math. Lect. Note Ser. 14 (1992), Exp. 5, 23 p.
Zentralblatt: 0802.17006
Description: Irreducible representations of class of algebras, including U(sl(2)), generalizing Block's method (probably also on subsequent papers of Bavula about some generalized Weyl algs)

Tensor homological minimal algebras, global dimension of the tensor product of algebras and of generalized Weyl algebras
Bull. Sci. Math. 120 (1996), no.3, 293-335.
MR 97f:16015

Dixmier's problem 5 for the Weyl algebra
DOI: 10.1016/j.jalgebra.2004.09.013
J. Algebra 283 (2005), N2, 604-621
arXiv:math.RA/0403037
Description: In introduction, a nice brief survey of known facts and developments related to Weyl algebras.

Simple derivations of differentiably simple Noetherian commutative rings in prime characteristic
DOI: 10.1090/S0002-9947-08-04567-4
arXiv:math.RA/0602632
Trans. Amer. Math. Soc. 360 (2008), 4007-4027

Bavula, V. and van Oystaeyen, F.

The simple modules of the Lie superalgebra $osp (1,2)$
J. Pure Appl. Algebra 150, No.1, 41-52 (2000)
Zentralblatt: 1006.17009
Zbl Review: A classification (up to irreducible elements of a certain Euclidean ring) of the simple modules of the Lie superalgebra $\text{osp}(1,2)$ (over an uncountable algebraically closed field of characteristic zero) is presented.
Availability: science.pdf

Baxter, R.J.

A direct proof of Kim's identities
J. Phys. A.: Math. Gen. 31 (1998), 1105-1108
Description: An identity appearing there involves generating functions for a number of representation of a given number as sum of squares.
Availability: a803n1.pdf; hardcopy

Baxter, W.E. and Martindale III, W.S.

Central closure of semiprime non-associative rings
DOI: 10.1080/00927877908822394
Communications in Algebra, Volume 7, Issue 11 1979 , pages 1103 - 1132
Availability: 780042801.pdf

Bayen, F. and Flato, M. and Fronsdal, C. and Lichnerowicz, A. and Sternheimer, D.

Deformation theory and quantization. I. Deformations of symplectic structures
DOI: 10.1016/0003-4916(78)90224-5
Annals of Physics Volume 111, Issue 1 , March 1978, Pages 61-110
Availability: annphys-1978.pdf

Bayer, Dave and Diaconis, Persi

Trailing the dovetail shuffle to its lair Ann. Appl. Probability 2 (1992), No.2, 294-313
Description: Cards shuffling is related to shuffles appearing in Hochschild and cyclic cohomology
Availability: trailing-the-dovetail.pdf

Bayer-Fluckiger, E. and Parimala, R. and Queguiner-Mathieu, A.

Pfister involutions
Proc. Indian Acad. Sci. Math. Sci. 113 (2003), no. 4, 365--377
Abstract: The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution is adjoint to a Pfister form. Moreover, cohomological invariants of those algebras with involution are discussed.

Bazlov, Yu.M.

The homology of infinite-dimensional Lie algebras in connection with Macdonald identity
DOI: 10.1007/BF02175822
Zapiski Nauchn. Sem. POMI 240 (1997), 5-17
Journal of Mathematical Sciences Issue Volume 96, Number 5 / October, 1999 Pages 3447-3454
Description: Correction of erroneous calculation of homology of Kac-Moody A_N(1) in Fuchs' book.

Beals, Robert

Algorithms for matrix groups and the Tits alternative
J. Computer Systems Sci. 58 (1999), 260-279
Zentralblatt: 0922.68064
Description: Tits alternative form the algorithmic point of view for groups over Q. Survey of computers usage in group theory.
Availability: Beals.pdf

Improved algorithms for the Tits alternative
(ed. W.M. Kantor et al.), Groups and computation III, de Gruyter, Ohio State Univ. Math. Res. Inst. Publ. 8 (2001), 63-77
MR 2002g:20085
Zentralblatt: 0992.20036
Availability: google book; 2001-improved/ (pages 63-66 only)

Becher, Karim Johannes

Alg\`ebres simples centrales \`a involution de premi\`ere esp\`ece
Linear Algebraic Groups and Related Structures Preprint Server 2003, 14 p.
Abstract: This article provides new and elementary proofs for some of the crucial theorems in the theory of central simple algebras with involution of the first kind. In the first place Albert's criterion for the existence of an involution of the first kind and Kneser's extension theorem for such involutions are presented in a unified way. These two results are retrieved as corollaries of a new theorem which gives a criterion to decide whether an antiautomorphism of a central simple algebra is an involution of the first kind. Two examples are given to indicate that the analogous approach cannot be applied to involutions of the second kind. Quaternion algebras give the easiest nontrivial examples of central simple algebras which carry an involution of the first kind. Albert has shown that any central simple algebra of dimension $16$ with involution of the first kind is a tensor product of two quaternion algebras. This theorem is presented here with a new proof essentially using basic linear algebra.

Beck, Jonathan Mock

Triples, Algebras and Cohomology
Ph.D. thesis, Columbia University, 1967
Reprints in Theory and Applications of Categories, No. 2 (2003) pp 1-59

Beck, R.E. and Kolman, B. and Stewart, I.N.

Computing the structure of a Lie algebra
Computers in Nonassociative Rings and Algebras (ed. R.E.Beck and B.Kolman), Acad. Press, 1977, 167-188

Beckenbach, Edwin and Bellman, Richard

Introduction to Inequalities
Random House, 1961
Description: Very elementary.
Availability: hardcopy (book); Kolkhoz (Russian edition)

a
m
a
z
o
n

Inequalities
URL: http://techlibrary.ru/books.htm http://da8.boom.ru/ct/algebra.htm
Springer, 1961
Mir, 1965
Availability: IneqsB.djvu (Russian translation)

Becker, Thomas and Kredel, Heinz and Weispfenning, Volker

Grobner Bases: A Computational Approach to Commutative Algebra
Springer, 1993, 574pp.
Description: http://www.powells.com/cgi-bin/biblio?show=Hardcover:New:0387979719:64.95
Availability: 46.50$

Becker, Thomas and Weispfenning, Volker

Gröbner Bases
Springer, 1993;

a
m
a
z
o
n

Beckerman, M.

Adaptive Cooperative Systems
Wiley, 1997; hardcover, 427 pp.
Availability: hardcopy (book)

Beerenwinkel, Niko and Eriksson, Nicholas and Sturmfels, Bernd

Evolution on distributive lattices
arXiv:q-bio/0511039

Beggs, E. J. and Brzezinski, Tomasz

The Van Est spectral sequence for Hopf algebras
Int. J. Geom. Meth. Modern Phys. 1(2004), N1-2, 33-48
Abstract: Various aspects of the de Rham cohomology of Hopf algebras are discussed. In particular, it is shown that the de Rham cohomology of an algebra with the differentiable coaction of a cosemisimple Hopf algebra with trivial 0-th cohomology group, reduces to the de Rham cohomology of (co)invariant forms. Spectral sequences are discussed and the van Est spectral sequence for Hopf algebras is introduced. A definition of Hopf-Lie algebra cohomology is also given.

Behn, Antonio and Correa, Iván and Hentzel, Irvin Roy

Semiprimality and nilpotency of nonassociative rings Satisfying x(yz) = y(zx)
DOI: 10.1080/00927870701665248
Comm. Algebra 36 (2008), N1, 132-141

Behrend, Kai and Xu, Ping and Zhang, Bin

Equivariant gerbes over compact simple Lie groups
math.SG/0306183, 6 pages
C. R. Acad. Sci. Paris, Ser. I 336 (2003) 251-256
Abstract: Using groupoid $S^1$-central extensions, we present, for a compact simple Lie group $G$, an infinite dimensional model of $S^1$-gerbe over the differential stack $G/G$ whose Dixmier-Douady class corresponds to the canonical generator of the equivariant cohomology $H_G^3 (G, Z)$.

Behrens, Ernst-August

Zur additiven Idealtheorie in nichtassoziativen Ringen
MZ 64 (1956), 169-182
Description: General reasonings about notions of prime and primitive ideals in nonassociative rings, related radicals.
Availability: behrens.pdf

Algebren
Bibliographishes Inst. Mannheim, 1965; paperback, 260 pp.
Availability: hardcopy (book)

Beidar, K.I. and Bresar, M. and Chebotar, M.A. and Martindale, W.S.

On Herstein's Lie map conjectures. III
DOI: 10.1006/jabr.2001.9076
J. Algebra 249 (2002), 59-94
Zentralblatt: 1019.16021
Description: Including Lie derivations of prime algebras.
Availability: 2002-liemap-3.pdf

Beidar, K. I. and Chebotar, M. A.

On Lie-admissible algebras whose commutator Lie algebras are Lie subalgebras of prime associative algebras
DOI: 10.1006/jabr.2000.8449
J. Algebra 233 (2000), 675-703
Availability: 2000-lie.pdf

When is a graded PI algebra a PI algebra?
Comm. Algebra 31 (2003), N6, 2951-

Beidar, K. I. and Chebotar, M. A. and Fong, Y. and Ke, W.-F.

On certain power-associative, Lie-admissible subalgebras of matrix algebras
DOI: 10.1007/s10958-005-0452-0
J. Math. Sci. 131 (2005), N5, 5939-5947

Beidar, K. I. and Latyshev, V. N. and Markov, V. T. and Mikhalev, A. V. and Skornyakov, L. A. and Tuganbaev, A. A.

Associative rings
DOI: 10.1007/BF01093433
J. Sov. Math. 38(1987), 1855-1929
Itogi Nauki Tekh., Ser. Algebra, Topologiya, Geom. 22, 3-115, 1984
Zentralblatt: 0564.16002
Description: A VINITI survey for RZhMat 1977-1983.
Availability: hardcopy; m2017321332371t3.pdf

Beidar, K.I. and Martindale III, W.S. and Mikhalev, A.V.

Rings with Generalized Identities
Marcel Dekker, 1996; hardcover, 522 pp.
Zentralblatt: 0847.16001
Availability: hardcopy (book); Kolkhoz; 1996-rings.djvu

a
m
a
z
o
n

Beidar, K.I. and Mikhalev, A.V.

Orthogonal completness and algebraic systems
Rus. Math. Surv. 40 (1985), N6, 51-95
Description: A big survey. Claims to generalize Los' theorem on ultraproducts, though the language and applicability is unclear.
Availability: hardcopy

On Malcev's theorem on elementary equivalence of linear groups
Contemp. Math. 131 Part I (1992), 29-35
Availability: hardcopy (book)

Generalized polynomial identities and rings which are sums of two subrings
DOI: 10.1007/BF00750549
Alg. and Logic 34 (1995), 1-5
Description: A sum of two PI-rings satisfying some special type identities, is PI.
Availability: 1995-generalized.pdf

The method of orthogonal completeness in the structure theory of rings
DOI: 10.1007/BF02366353
J. Math. Sci. 73 (1995), N1, 1-46
Sovr. Mat. Prilozh. Vol. 4, Algebra-1, VINITI, 1993

Beidar, K I and Mikhalev, A V and Chebotar', M A

Functional identities in rings and their applications
DOI: 10.1070/RM2004v059n03ABEH000735
Russ. Math. Surv. 59 (2004), N3, 403-428
MR 2116534
Zentralblatt: 1078.16017
Description: A survey, including Lie and Jordan mappings. Functinal identities include additive maps. All power-associative Lie-admissible structures on Lie ideals of prime algebras and Lie algebars of skew-symmetric elements.
Availability: 2004-functional.pdf

Beidar, K.I. and Mikhalev, A.V. and Puninskii, G.E.

Logical aspects of ring and module theory
Fund. Prikl. Mat. 1(1995), N1, 1-62
Description: A VINITI-style survey. Particularly, categoricity, stability, elementary equivalence, etc. of rings and algebras.
Availability: 95101.ps

Beidar, K.I. and Pikhtilkov, S.A.

The primary radical of special Lie algebras
Rus. Math. Surv. circa 1993
Zentralblatt: 0833.17006
Description: Theorem 4. Let L be a generalized special Lie algebra such that all its abelian subalgebras are finite-dimensional. Then L is finite-dimensional.

The prime radical of special Lie algebras (in Russian)
Fundam. Prikl. Matem. 6(2000), N3, 643-648
Zentralblatt: 1001.17004
Availability: bejdpikh.ps

Beidar, Konstantin I. and Wisbauer, Robert

On uniform bounds of primeness in matrix rings
URL: http://www.austms.org.au/Publ/JAustMS/V76P2/d122.html http://www.math.uni-duesseldorf.de/~wisbauer/
J. Aust. Math. Soc. 76 (2004), 167-174
Availability: bound.pdf; hardcopy

Beidar, K. I. and Zaitsev, M. V. (=Zaicev) and Pikhtilkov, S. A.

Lie algebras with the maximality condition for abelian subalgebras
Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2002, no. 5, 27--32
Description: Maximality conditions for abelian subalgebras for a (generalized) special Lie algebra implies finite-dimensionality.
Availability: hardcopy

Beilinson, Alexander and Drinfeld, Vladimir

Chiral Algebras
URL: http://www.ams.org/bookstore-getitem/isbn=0-8218-3528-9 http://www.math.utexas.edu/~benzvi/BD/CHA.ps.gz (draft) http://www.math.uchicago.edu/~mitya/langlands.html
AMS Colloq. Publ. 51 (2004)
Description: These are generalization of vertex operator algebras. Also related to Poisson algebras.

a
m
a
z
o
n

Opers
arXiv:math.AG/0501398
Description: An elementary introduction.

Beilinson, Alexander and Ginzburg, Victor and Soergel, Wolfgang

Koszul duality patterns in representation theory
J. Amer. Math. Soc. 9(1996), No.2, 473-527
MR 96k:17010
Zentralblatt: 0864.17006

Beilinson, A.A. and Manin, Yu.I. and Schechtman, V.V.

Sheaves of the Virasoro and Neveu-Schwarz algebras
Lect. Notes Math. (K-theory, arithmetic and geometry) 1289(1987), 52-66
MR 89j:58039
Availability: hardcopy; amazon

Beke, Tibor

Isoperimetric inequalities and the Friedlander-Milnor conjecture
DOI: 10.1515/crll.2005.2005.587.27
JRAM 2005, Issue 587, Pages 27-47
arXiv:math.KT/0403426
Description: Behaviour of cohomology under ultraproduct.

Belaga, Edward G.

Reflecting on the 3x+1 mystery. Outline of a scenario - improbable or realistic?
Preprint, December 1998
Availability: 98049.pdf

Belavin, A.A. and Drinfeld, V.G.

Solutions of the classical Yang-Baxter equation for simple Lie algebras
DOI: 10.1007/BF01081585
Funct. Anal. Appl. 16 (1982), N3, 159-180
Zentralblatt: 0511.22011
Description: It is explained how CYBE related to quasi-Frobenius Lie algebras (those having a nondegenerate 2-cocycle).
Availability: 1982-solutions.pdf

On the classical Young-Baxter equation for simple Lie algebras
Funct. Anal. Appl. 17, 220-221 (1983)
Funkts. Anal. Prilozh. 17, No.3, 69-70 (1983)
Zentralblatt: 0533.22014

Triangle equations and simple Lie algebras
Sov. Sci. Rev., Sect. C, Math. Phys. Rev. 4, 93-165 (1984)
Classic Reviews in Mathematics and Mathematical Physics. 1. Amsterdam: Harwood Academic Publishers. vii, 91 p. (1998)
Zentralblatt: 0553.58040
Description: CYBE

Belegradek, Oleg V.

The model theory of unitriangular groups
Ann. Pure Appl. Logic 68 (1994), No.3, 225-261
Zentralblatt: 0807.03025

Model theory of unitriangular groups
Model Theory and Applications, AMS Transl. 195 (1999), 1-116
Zentralblatt: 0931.03053
Description: A survey.

Model theory of locally free algebras
Model Theory and Applications, AMS Transl. 195 (1999), 117-143
MR 89i:03056

Belinfante, Johan G.F. and Kolman, Bernard

A survey of Lie groups and Lie algebras with applications and computational methods
SIAM, Society for Industrial and Applied Mathematics. IX, 164 p. (1972)
Zentralblatt: 0244.22008
Availability: Kolkhoz's obmennik?

Belinfante, J.G. and Kolman, B. and Smith, H.A.

An introduction to Lie groups and Lie algebras, with applications
SIAM Review 8 (1966), N1, 11-46
Description: A pedestrian intro into Lie group-Lie algebra correspondence, which may be useful in deformation-theoretic framework.
Availability: intro-lie.djvu

Belitskii, Genrich and Lipyanski, Ruvim and Sergeichuk, Vladimir

Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild
Lin. Alg. Appl. 407 (2005), 249-262
Description: Problem of classification of Lie algebras with central commutator subalgebra of dimension 3 is wild. Description of such Lie algebras with dim L^2 = 1 and 2.
Availability: science-2.pdf; arXiv:0709.2463

Belitskii, Genrich R. and Sergeichuk, Vladimir V.

Congruence of multilinear forms
Linear Algebra Appl. 418 (2006), no. 2-3, 751--762
(me)
Availability: hardcopy

Bell, Allen D. and Farnsteiner, Rolf

On the theory of Frobenius extensions and its application to Lie superalgebras
DOI: 10.2307/2154275
TAMS 335 (1993), No.1, 407-424

Bell, Howard E. and Klein, Abraham A.

Extremely noncommutative elements in rings
DOI: 10.1007/s00605-007-0505-1
Monatshefte für Mathematik Volume 153, Number 1 / January, 2008 Pages 19-24
Description: Associative rings and algebars with property a and b commute => b is a polynomial in a. Such rings (but not algebras!) are either finite or commutative.

Bell, J.L. and Slomson, A.B.

Models and Ultraproducts
2nd revised printing, North-Holland, 1971; paperback, 322 pp.

a
m
a
z
o
n

Bell, E.T.

Men of Mathematics, Vol. I, II
Penguin Books, 1953; paperback, small format, 646 pp.
Availability: hardcopy (books)

a
m
a
z
o
n

Bell, Howard E.

Pacific J. Math. 59 (1975), no.2, 345-348
MR 52#8197
Description: Any infinite alternative ring contains an infinite commutative subring (generalization of Laffey's theorm for associative rings).

Higher derivatives and finiteness in rings
Math. J. Okayama Univ. 41 (1999), 21-25

Bellman, R.

Introduction to Matrix Analysis
MGH, 1960
2nd ed., SIAM, 1997
Availability: Kolkhoz (1st ed.); Kolkhoz' obmennik (2nd ed.)

a
m
a
z
o
n

Vvedenie v teoriyu matric
(in Russian)
Availability: Kolkhoz

a
m
a
z
o
n

o
z
o
n

Belohlavek, R.

Birkhoff variety theorem and fuzzy logic
Archive for Mathematical Logic Volume 42, Number 8 November 2003, 781 - 790

Belonogov, V.A.

Predstavleniya i charaktery v teorii konechnykh grupp
Sverdlovsk, 1990 (in Russian)
Availability: Kolkhoz

Zadachnik po teorii grupp
Nauka, Moscow, 2000 (in Russian)
Availability: Kolkhoz; 2000-zadachnik.djvu

Belousov, V.D.

Osnovy teorii kvazigrupp i lup
Nauka, 1967 (in Russian)
Availability: Kolkhoz

Belousov, Valentin Danilovich and Belyavksaya, Galina Borisovna

Latinskie kvadraty, kvazigruppy i ikh prilozheniya
Shtinica, Kishinev, 1989

Belov, A. Ya.

On a Shirshov basis of relatively free algebras of complexity n
DOI: 10.1070/SM1989v063n02ABEH003279
Math. USSR Sb. 63 (1989), no.2, 363--374
MR 89d:16022
Zentralblatt: 0659.16012
Availability: MSB_63_2_A07.pdf

Some estimations for nilpotence of nil-algebras over a field of an arbitrary characteristic and height theorem
DOI: 10.1080/00927879208824497
Comm. Algebra 20 (1992), N10, 2919-2922
Availability: 780111928_content.pdf

About height theorem
DOI: 10.1080/00927879508825416
Comm. Algebra 23 (1995), N9, 3551-3553
Availability: 780027621.pdf

No associative PI-algebra coincides with its commutant
DOI: 10.1023/B:SIMJ.0000007472.85188.56
Siberian Math. J. 44 (2003), N6, 969-980
MR 2034931
Zentralblatt: 1054.16015
Availability: hardcopy

T