Non-abelian tensor product and homology of Lie superalgebras

被引：18

作者：

Garcia-Martinez, Xabier ^{[1
]}

Khraaladze, Emzar ^{[2
]}

Ladra, Manuel ^{[1
]}

机构：

[1] Univ Santiago de Compostela, IMAT, Dept Algebra, Santiago De Compostela 15782, Spain

[2] Tbilisi State Univ, A Razmadze Math Inst, GE-0177 Tbilisi, Georgia

来源：

JOURNAL OF ALGEBRA | 2015年 / 440卷

基金：

美国国家科学基金会;

关键词：

Lie superalgebras; Associative superalgebras; Non-abelian tensor and exterior products; Non-abelian homology; Cyclic homology; Hopf formula; Crossed module; CENTRAL EXTENSIONS; COHOMOLOGY; ALGEBRAS;

D O I：

10.1016/j.jalgebra.2015.05.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the non-abelian tensor product of Lie superalgebras and study some of its properties. We use it to describe the universal central extensions of Lie superalgebras. We present the low-dimensional non-abelian homology of Lie superalgebras and establish its relationship with the cyclic homology of associative superalgebras. We also define the non-abelian exterior product and give an analogue of Miller's theorem, Hopf formula and a six-term exact sequence for the homology of Lie superalgebras. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：464 / 488

页数：25

共 23 条

[11]

Hilton P. J., 1997, GRAD TEXTS MATH, V4

[12] Non-abelian homology of Lie algebras [J].

Inassaridze, N ;

Khmaladze, E ;

Ladra, M .

GLASGOW MATHEMATICAL JOURNAL, 2004, 46 :417-429

[13] Second homology of Lie superalgebras [J].

Iohara, K ;

Koga, Y .

MATHEMATISCHE NACHRICHTEN, 2005, 278 (09) :1041-1053

[14] LIE SUPER-ALGEBRAS [J].

KAC, VG .

ADVANCES IN MATHEMATICS, 1977, 26 (01) :8-96

[15] A KUNNETH FORMULA FOR THE CYCLIC COHOMOLOGY OF Z/2-GRADED ALGEBRAS [J].

KASSEL, C .

MATHEMATISCHE ANNALEN, 1986, 275 (04) :683-699

[16] CENTRAL EXTENSIONS OF LIE-ALGEBRAS [J].

KASSEL, C ;

LODAY, JL .

ANNALES DE L INSTITUT FOURIER, 1982, 32 (04) :119-142

[17] THE 2ND HOMOLOGY GROUP OF A GROUP - RELATIONS AMONG COMMUTATORS [J].

MILLER, C .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 3 (04) :588-595

[18]

Musson I. M., 2012, GRAD STUD MATH, V131

[19]

Neher E, 2003, MATH APPL, V555, P141

[20] On the non-abelian tensor product of Lie algebras [J].

Salemkar, Ali Reza ;

Tavallaee, Hamid ;

Mohammadzadeh, Hamid ;

Edalatzadeh, Behrouz .

LINEAR & MULTILINEAR ALGEBRA, 2010, 58 (03) :333-341

← 1 2 3 →