P.i algebras with Hopf algebra actions

JOURNAL OF ALGEBRA

卷:214

Article

Berele, A ; Bergen, J

关键词: pi algebra;    Hopf algebra action;    group action;    group grading;    verbally prime;    verbally semiprime;   

DOI  :  10.1006/jabr.1998.7707

来源: Elsevier

【 摘 要 】

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 A/N 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. algebras, up to equivalence. This paper generalizes the work of A. R. Kerner (1985, Math. USSR Izv. 25). (C) 1999 Academic Press.

【 授权许可】

Free