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

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.

26 pages; minor misprints were corrected

Cited by in corpus (7)

• Amitsur's conjecture for polynomial H-identities of H-module Lie algebras
• Algebras simple with respect to a Taft algebra action
• Structure of H-(co)module Lie algebras
• Lie algebras simple with respect to a Taft algebra action
• On $H$-simple not necessarily associative algebras
• (Co)module algebras and their generalizations
• Derivations, gradings, actions of algebraic groups, and codimension growth of polynomial identities