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arXiv · 1112.6245

Graded polynomial identities, group actions, and exponential growth of Lie algebras

Alexey Sergeevich Gordienko
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Abstract

Consider a finite dimensional Lie algebra L with an action of a finite group G over a field of characteristic 0. We prove the analog of Amitsur's conjecture on asymptotic behavior for codimensions of polynomial G-identities of L. As a consequence, we prove the analog of Amitsur's conjecture for graded codimensions of any finite dimensional Lie algebra graded by a finite Abelian group.

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Alexey Sergeevich Gordienko. 2013-03-08. Graded polynomial identities, group actions, and exponential growth of Lie algebras. https://doi.org/10.1016/j.jalgebra.2012.05.021

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