On stem covers and the universal central extensions of Lie crossed modules

Abstract

In this article, we investigate stem covers and the universal central extensions of Lie crossed modules. In particular, a cover for the direct sum of two Lie crossed modules in term of given covers of them will be constructed. Using the results obtained, we give some properties of covers and the universal relative central extensions of pairs of Lie algebras.

Keywords:

• Crossed module
• Lie algebra
• relative central extension
• second homology
• stem cover

2010 Mathematics subject classification:

• 18B99
• 20E34
• 20N99

Acknowledgments

The authors thank the referee for his/her valuable suggestions that helped improve the paper.