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arXiv · 1207.1699

Amitsur's conjecture for polynomial H-identities of H-module Lie algebras

Alexey Sergeevich Gordienko
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Abstract

Consider a finite dimensional H-module Lie algebra L over a field of characteristic 0 where H is a Hopf algebra. We prove the analog of Amitsur's conjecture on asymptotic behavior for codimensions of polynomial H-identities of L under some assumptions on H. In particular, the conjecture holds when H is finite dimensional semisimple. As a consequence, we obtain the analog of Amitsur's conjecture for graded codimensions of any finite dimensional Lie algebra graded by an arbitrary group and for G-codimensions of any finite dimensional Lie algebra with a rational action of a reductive affine algebraic group G by automorphisms and anti-automorphisms.

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Alexey Sergeevich Gordienko. 2012-07-06. Amitsur's conjecture for polynomial H-identities of H-module Lie algebras. https://doi.org/10.1090/s0002-9947-2014-06059-5

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