The Bogomolov multiplier of Lie algebras

TL;DR

This paper extends the concept of Bogomolov multipliers to Lie algebras, computes these for various classes including Abelian, Heisenberg, nilpotent, and some simple complex Lie algebras, advancing algebraic understanding.

Contribution

It introduces the notion of Bogomolov multipliers for Lie algebras and provides explicit computations for several important classes.

Findings

Bogomolov multipliers for Abelian, Heisenberg, and nilpotent Lie algebras of class ≤ 6

Computed Bogomolov multipliers for some simple complex Lie algebras

Extended the concept of CP-extensions to Lie algebras

Abstract

In this paper, we extend the notion of the Bogomolov multipliers and the CP-extensions to Lie algebras. Then we compute the Bogomolov multipliers for Abelian, Heisenberg and nilpotent Lie algebras of class at most 6. Finally we compute the Bogomolov multipliers of some simple complex Lie algebras.