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

DOI10.1016/j.jpaa.2012.11.001zbMath1286.16023arXiv1203.5384OpenAlexW2963358632WikidataQ122983322 ScholiaQ122983322MaRDI QIDQ2376583

Alexei S. Gordienko

Publication date: 24 June 2013

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.5384

zbMATH Keywords

Hopf algebras\(H\)-module algebrascodimension sequencesgraded codimensionsPI-algebrasgraded polynomial identitiesexponents of varietiesAmitsur conjecture\(H\)-identitiesgeneralized Hopf actions

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Automorphisms and endomorphisms (16W20) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Graded rings and modules (associative rings and algebras) (16W50) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Hopf algebras and their applications (16T05)

Related Items (33)

\((\delta,\varepsilon)\)-differential identities of \(UT_m(F)\) ⋮ Kemer's theory for \(H\)-module algebras with application to the PI exponent ⋮ Graded polynomial identities as identities of universal algebras ⋮ Differential identities, \(2 \times 2\) upper triangular matrices and varieties of almost polynomial growth ⋮ Star-polynomial identities: computing the exponential growth of the codimensions ⋮ The exponent for superalgebras with superinvolution ⋮ Codimension growth of Lie algebras with a generalized action ⋮ Actions of Ore extensions and growth of polynomialH-identities ⋮ *-Graded Capelli polynomials and their asymptotics ⋮ Capelli identities on algebras with involution or graded involution ⋮ Differential polynomial identities of upper triangular matrices of size three ⋮ Varieties of group graded algebras with graded involution of almost polynomial growth ⋮ Graded group actions and generalized \(H\)-actions compatible with gradings ⋮ Polynomial identities with involution, superinvolutions and the Grassmann envelope ⋮ On weak equivalences of gradings ⋮ Asymptotics of \(H\)-identities for associative algebras with an \(H\)-invariant radical. ⋮ Asymptotics of graded codimension of upper triangular matrices ⋮ Classifying \(G\)-graded algebras of exponent two ⋮ On the factorability of the ideal of \(\ast\)-graded polynomial identities of minimal varieties of PI \(\ast\)-superalgebras ⋮ \(\ast\)-Superalgebras and exponential growth ⋮ Distinguishing simple algebras by means of polynomial identities ⋮ On group gradings on PI-algebras. ⋮ Semigroup graded algebras and graded PI-exponent ⋮ Derivations, gradings, actions of algebraic groups, and codimension growth of polynomial identities. ⋮ Minimal varieties of PI-superalgebras with graded involution ⋮ A characterization of superalgebras with pseudoinvolution of exponent 2 ⋮ On H-simple not necessarily associative algebras ⋮ Equivalences of (co)module algebra structures over Hopf algebras ⋮ Understanding star-fundamental algebras ⋮ Amitsur’s conjecture for polynomial 𝐻-identities of 𝐻-module Lie algebras ⋮ Algebras simple with respect to a Sweedler's algebra action ⋮ Algebras simple with respect to a Taft algebra action. ⋮ On the identical relations of associative and Lie algebras equipped with an action

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