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

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 $q$.