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

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

2012-03-24

arxiv.org/abs/1203.5384v2

Mathematics

Rings and Algebras

21 pages; introduction was improved; references were reordered; Section 3 was divided into subsections

Scientific paper

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.

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