Kemer's theory for H-module algebras with application to the PI exponent

JOURNAL OF ALGEBRA

卷:457

Article

Karasik, Yaakov¹ 

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

关键词: Graded algebra;    Polynomial identity;    Hopf algebra;    Exponent;   

DOI  :  10.1016/j.jalgebra.2016.02.021

来源: Elsevier

【 摘 要 】

Let H be a semisimple finite dimensional Hopf algebra over a field F of zero characteristic. We prove three major theorems. 1. The Representability theorem which states that every H-module (associative) F-algebra W satisfying an ordinary PI, has the same H-identities as the Grassmann envelope of an H circle times(FZ/2Z)*-module algebra which is finite dimensional over a field extension of F. 2. The Specht problem for H-module (ordinary) PI algebras. That is, every H T-ideal Gamma which contains an ordinary PI contains H-polynomials f(1),. . .,f(s) which generate Gamma as an H T-ideal. 3. Amitsur's conjecture for H-module algebras, saying that the exponent of the H-codimension sequence of an ordinary PI H-module algebra is an integer. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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