Actions of pointed Hopf algebras with reduced pi invariants

Authors:
Piotr Grzeszczuk and Malgorzata Hryniewicka

Journal:
Proc. Amer. Math. Soc. **135** (2007), 2381-2389

MSC (2000):
Primary 16R20, 16S40, 16W30

DOI:
https://doi.org/10.1090/S0002-9939-07-08769-2

Published electronically:
March 29, 2007

MathSciNet review:
2302559

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an -module algebra, where is a pointed Hopf algebra acting on finitely of dimension . Suppose that for every nonzero -stable left ideal of . It is proved that if satisfies a polynomial identity of degree , then satisfies a polynomial identity of degree provided at least one of the following additional conditions is fulfilled:

- is semiprime and is almost central in ,
- is reduced.

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Additional Information

**Piotr Grzeszczuk**

Affiliation:
Faculty of Computer Science, Technical University of Białystok, Wiejska 45A, 15-351 Białystok, Poland

Email:
piotrgr@pb.bialystok.pl

**Malgorzata Hryniewicka**

Affiliation:
Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland

Email:
margitt@math.uwb.edu.pl

DOI:
https://doi.org/10.1090/S0002-9939-07-08769-2

Received by editor(s):
January 8, 2006

Received by editor(s) in revised form:
April 25, 2006

Published electronically:
March 29, 2007

Additional Notes:
The first author was supported by Polish KBN grant No. 1 P03A 032 27

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.