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arXiv · 1404.6942

Finite generation of Lie algebras associated to associative algebras

Adel Alahmedi·Hamed Alsulami·S. K. Jain·Efim Zelmanov
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Abstract

Let $F$ be a field of characteristic not $2$ . An associative $F$-algebra $R$ gives rise to the commutator Lie algebra $R^{(-)}=(R,[a,b]=ab-ba).$ If the algebra $R$ is equipped with an involution $*:R\rightarrow R$ then the space of the skew-symmetric elements $K=\{a \in R \mid a^{*}=-a \}$ is a Lie subalgebra of $R^{(-)}.$ In this paper we find sufficient conditions for the Lie algebras $[R,R]$ and $[K,K]$ to be finitely generated.

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Adel Alahmedi, Hamed Alsulami, S. K. Jain, Efim Zelmanov. 2014-04-28. Finite generation of Lie algebras associated to associative algebras. https://arxiv.org/abs/1404.6942

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