Homology, Homotopy and Applications

Volume 1 (1999)

Number 1

Non-abelian tensor and exterior products modulo $q$ and universal $q$-central relative extension of Lie algebras

Pages: 187 – 204

DOI: http://dx.doi.org/10.4310/HHA.1999.v1.n1.a9

Author

Emzar Khmaladze (A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Republic of Georgia)

Abstract

The notions of tensor end exterior products modulo $q$ of two crossed $P$-modules, where $q$ is a positive integer and $P$ is a Lie algebra, are introduced and some properties are established. The condition for the existence of a universal $q$-central relative extension of a Lie epimorphism is given and this extension is described as an exterior product modulo $q$.

Keywords

Lie algebra, tensor product, exterior product, crossed module, universal extension

2010 Mathematics Subject Classification

18G50

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