Low-dimensional non-abelian Leibniz cohomology

被引：9

作者：

Manuel Casas, Jose ^{[1
]}

Khmaladze, Emzar ^{[2
]}

Ladra, Manuel ^{[3
]}

机构：

[1] Univ Vigo, EUIT Forestal, Dept Matemat Aplicada 1, Pontevedra 36005, Spain

[2] A Razmadze Math Inst, Dept Algebra, GE-0193 Tbilisi, Georgia

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

来源：

FORUM MATHEMATICUM | 2013年 / 25卷 / 03期

关键词：

Leibniz algebra; crossed module; non-abelian cohomology; derivation and anti-derivation; TENSOR PRODUCT; HOMOLOGY; ALGEBRAS;

D O I：

10.1515/FORM.2011.124

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct the zero and first non-abelian cohomologies of Leibniz algebras with coefficients in crossed modules, which differ from those of Gnedbaye and generalize the zero and first Leibniz cohomologies of Loday and Pirashvili. We also introduce the second non-abelian Leibniz cohomology and describe its relationship with extensions of Leibniz algebras by crossed modules. We obtain a nine-term exact non-abelian cohomology sequence. For Lie algebras we compare the non-abelian Leibniz and Lie cohomologies.

引用

页码：443 / 469

页数：27

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