Non-abelian tensor product and homology of Lie superalgebras

JOURNAL OF ALGEBRA

卷:440

Article

Garcia-Martinez, Xabier¹  Khraaladze, Emzar²  Ladra, Manuel¹ 

[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

关键词: Lie superalgebras;    Associative superalgebras;    Non-abelian tensor and exterior products;    Non-abelian homology;    Cyclic homology;    Hopf formula;    Crossed module;   

DOI  :  10.1016/j.jalgebra.2015.05.027

来源: Elsevier

【 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.

【 授权许可】

Free