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


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


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 $q$.


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

2010 Mathematics Subject Classification


Published 1 January 1999