Bogomolov multiplier and the Lazard correspondence

Abstract

In this paper, we extend the notion of CP covers for groups to the class of Lie algebras, and show that despite the case of groups, all CP covers of a Lie algebra are isomorphic. Moreover we show that CP covers of groups and Lie rings which are in Lazard correspondence, are in Lazard correspondence too, and the Bogomolov multipliers of the group and the Lie ring are isomorphic.

Keywords:

• Baker–Campbell–Hausdorff formula
• Bogomolov multiplier
• commutativity-preserving defining pair
• CP cover
• Lazard correspondence

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 17B05
• Secondary 17B99