Amitsur's conjecture for polynomial H-identities of H-module Lie algebras
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.
Keywords
Cite
@article{arxiv.1207.1699,
title = {Amitsur's conjecture for polynomial H-identities of H-module Lie algebras},
author = {Alexey Sergeevich Gordienko},
journal= {arXiv preprint arXiv:1207.1699},
year = {2017}
}
Comments
38 pages; this article is a generalization of M.V. Zaicev's paper (Izv. Math, 2002) and the author's arXiv:1112.6245; the outline of the proof of the main result is the same as in those articles, however we have to deal with new phenomena that appear in H-module algebras; the introductory part, where we give a survey of what has already been done, overlaps with arXiv:1203.5384