Amitsur's conjecture for associative algebras with a generalized Hopf action

By Alexey Gordienko. 2012

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We prove the analog of Amitsur's conjecture on asymptotic behavior for codimensions of several generalizations of polynomial identities for finite dimensional associative algebras over a field of characteristic 0, including G-identities for any finite (not necessarily Abelian) group G and H-identities for a finite dimensional semisimple Hopf algebra H. In addition, we prove that the Hopf PI-exponent of Sweedler's 4-dimensional algebra with the action of its dual equals 4.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

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