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

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

2011-12-29

arxiv.org/abs/1112.6245v1

Mathematics

Rings and Algebras

26 pages

Scientific paper

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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