# Bogomolov multiplier and the Lazard correspondence

## TL;DR

This paper extends the concept of CP covers from groups to Lie algebras, demonstrating their isomorphism and establishing a correspondence between Bogomolov multipliers of groups and Lie rings via Lazard correspondence.

## Contribution

It introduces CP covers for Lie algebras, proves their uniqueness, and links Bogomolov multipliers across group and Lie ring structures through Lazard correspondence.

## Key findings

- All CP covers of a Lie algebra are isomorphic.
- CP covers of Lazard-related groups and Lie rings are in Lazard correspondence.
- Bogomolov multipliers are isomorphic under Lazard correspondence.

## Abstract

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