Some New Parallels Between Groups and Lie Algebras, or What Can Be Simpler than Multiplication Table?

Kunyavskiı̆, Boris

doi:10.4171/news/118/4

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2023

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Cited by 2 publications

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“…Theorem 1.1. Let L be a finite dimensional Lie algebra with a free presentation As an application we answer a couple of questions of Kunyavskiȋ [4]. He asked the following questions for finite dimensional Lie algebras L: Two Lie algebras L and K are said to be isoclinic if there exist isomorphisms α : L/Z(L) → K/Z(K) and β : L ′ → K ′ such that the following diagram commutes.…”

Section: Introductionmentioning

confidence: 99%

Bogomolov Multiplier of Lie algebras

Rai¹

2023

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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.

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Section: Introductionmentioning

confidence: 99%