Bogomolov Multiplier of Lie algebras

Abstract

In the work of Rostami et al., the Bogomolov multiplier of a Lie algebra L over a field Ω is defined as a particular factor of a subalgebra of the exterior product L ∧ L. If L is finite dimensional, we identify this object as a certain subgroup of the second cohomology group H 2 (L, Ω) by deriving a Hopf-Type formula. As an application, we affirmatively answer two questions posed by Kunyavskiȋ regarding the invariance of the Bogomolov multiplier under isoclinism of Lie algebras and the existence of a family of Lie algebras with Bogomolov multipliers of unbounded dimension.