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

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