Non-abelian tensor product of precrossed modules in Lie algebras, structure and applications

Abstract

In the present paper, we introduce the notion of non-abelian tensor product of a given precrossed module by one of its ideals. We use this concept to study the second homology and the nilpotent multiplier of a precrossed module. We also describe the Ganea term for the c-nilpotent multiplier and the universal central extension of precrossed modules in term of the non-abelian tensor product.

Keywords:

• Nilpotent multiplier
• non-abelian tensor product
• precrossed module

2020 Mathematics Subject Classification:

• 18G50
• 18G60
• 19C09

Acknowledgment

The authors would like to thank the referee for valuable comments and suggestions.