About Leibniz cohomology and deformations of Lie algebras

被引：13

作者：

Fialowski, A. ^{[1
]}

Magnin, L. ^{[2
]}

Mandal, A. ^{[3
]}

机构：

[1] Eotvos Lorand Univ, Inst Math, H-1117 Budapest, Hungary

[2] Univ Bourgogne, Inst Math Bourgogne, UMR CNRS 5584, F-21078 Dijon, France

[3] Univ Luxembourg, Math Res Unit, L-1359 Luxembourg, Luxembourg

来源：

JOURNAL OF ALGEBRA | 2013年 / 383卷

关键词：

Leibniz algebra; Lie algebra; Cohomology; Versal deformation;

D O I：

10.1016/j.jalgebra.2013.02.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We compare the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones by a very elementary approach. The comparison gives some conditions, which are easy to verify for a given Lie algebra, for deciding whether it has more Leibniz deformations than just the Lie ones. We also give the complete description of the Leibniz (and Lie) universal infinitesimal deformation of the 4-dimensional diamond Lie algebra, used in the WZW model, and study the case of its 5-dimensional analogue by computing Massey products. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：63 / 77

页数：15

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