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P.I. Algebras with Hopf Algebra Actions

✍ Scribed by Allan Berele; Jeffrey Bergen

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 123 KB
Volume: 214
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7707

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✦ Synopsis

If A is a p.i. algebra in characteristic zero with action from a finite-dimensional semisimple Hopf algebra H, then A has a nilpotent H-ideal N such that ArN will be H-verbally semiprime. Every H-verbally semiprime algebra is H-p.i. equivalent to a direct sum of H-verbally prime algebras. In the case of a finite group action or a grading by an abelian group, we show that the sum can be taken to be finite. In the case of an action by a finite cyclic group G, we classify all G-p.i. Ž algebras, up to equivalence. This paper generalizes the work of A. R. Kerner 1985, . Math. USSR Iz¨. 25 .

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