The Bogomolov multiplier of 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 complex simple and semisimple Lie algebras.