Amitsur¡¯s conjecture for associative algebras with a generalized Hopf action

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• 作者：A.S. Gordienko ^{asgordienko@mun.ca gordienko.a.s@gmail.com}
• 关键词：Primary ; 16R10 ; Secondary ; 16R50 ; 16W20 ; 16W22 ; 16W50 ; 16T05 ; 20C30
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2013
• 出版时间：August, 2013
• 年：2013
• 卷：217
• 期：8
• 页码：1395-1411
• 全文大小：480 K

文摘

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 -identities for any finite (not necessarily Abelian) group? and -identities for a finite dimensional semisimple Hopf algebra?. In addition, we prove that the Hopf PI-exponent of Sweedler¡¯s -dimensional algebra with the action of its dual equals 4.