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arXiv · 1212.1321

Asymptotics of H-identities for associative algebras with an H-invariant radical

Alexey Sergeevich Gordienko
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Abstract

We prove the existence of the Hopf PI-exponent for finite dimensional associative algebras $A$ with a generalized Hopf action of an associative algebra $H$ with $1$ over an algebraically closed field of characteristic $0$ assuming only the invariance of the Jacobson radical $J(A)$ under the $H$-action and the existence of the decomposition of $A/J(A)$ into the sum of $H$-simple algebras. As a consequence, we show that the analog of Amitsur's conjecture holds for $G$-codimensions of finite dimensional associative algebras over a field of characteristic $0$ with an action of an arbitrary group $G$ by automorphisms and anti-automorphisms and for differential codimensions of finite dimensional associative algebras with an action of an arbitrary Lie algebra by derivations.

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Alexey Sergeevich Gordienko. 2015-05-18. Asymptotics of H-identities for associative algebras with an H-invariant radical. https://arxiv.org/abs/1212.1321

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