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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: March 29, 2007
MathSciNet review: 2302559
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Abstract: Let $ R$ be an $ H$-module algebra, where $ H$ is a pointed Hopf algebra acting on $ R$ finitely of dimension $ N$. Suppose that $ L^H\neq 0$ for every nonzero $ H$-stable left ideal of $ R$. It is proved that if $ R^H$ satisfies a polynomial identity of degree $ d$, then $ R$ satisfies a polynomial identity of degree $ dN$ provided at least one of the following additional conditions is fulfilled:

  1. $ R$ is semiprime and $ R^H$ is almost central in $ R$,
  2. $ R$ is reduced.
If we also assume that $ R^H$ is central, then $ R$ satisfies the standard polynomial identity of degree $ 2[\sqrt{N}]$, where $ [\sqrt{N}]$ is the greatest integer in $ \sqrt{N}$.


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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: http://dx.doi.org/10.1090/S0002-9939-07-08769-2
PII: S 0002-9939(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.