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arXiv · 2301.01963

Bogomolov Multiplier of Lie algebras

Pradeep K. Rai
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Abstract

In the work of Rostami et al., the Bogomolov multiplier of a Lie algebra $L$ over a field $\Omega$ is defined as a particular factor of a subalgebra of the exterior product $L \wedge L$. If $L$ is finite dimensional, we identify this object as a certain subgroup of the second cohomology group $H^2(L, \Omega)$ by deriving a Hopf-Type formula. As an application, we affirmatively answer two questions posed by Kunyavskii 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.

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Pradeep K. Rai. 2023-01-05. Bogomolov Multiplier of Lie algebras. https://arxiv.org/abs/2301.01963

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