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Graded polynomial identities, group actions, and exponential growth of Lie algebras. (English) Zbl 1302.17005

Summary: 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 Amitsu’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.

MSC:

17B01 Identities, free Lie (super)algebras
17B70 Graded Lie (super)algebras
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
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