Cohomology of 3-dimensional color Lie algebras

被引：17
|
作者：
Piontkovski, Dmitri
Silvestrov, Sergei D.
机构：
[1] Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden
[2] State Univ, Higher Sch Econ, Dept High Math Econ, Moscow 101990, Russia
来源：
JOURNAL OF ALGEBRA | 2007年 / 316卷 / 02期
关键词：
color Lie algebras; Koszul algebras; quadratic algebras; cohomology;
D O I：
10.1016/j.jalgebra.2006.11.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop the cohomology theory of color Lie algebras due to Scheunert-Zhang in a framework of non-homogeneous quadratic Koszul algebras. In this approach, the Chevalley-Eilenberg complex of a color Lie algebra becomes a standard Koszul complex for its universal enveloping algebra, providing a constructive method for computation of cohomology. As an application, we compute cohomologies with trivial coefficients of Z(2)(n)-graded 3-dimensional color Lie algebras. 2 (c) 2006 Elsevier Inc. All rights reserved.
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页码：499 / 513
页数：15
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