Actions of pointed Hopf algebras with reduced pi invariants
Authors:
Piotr Grzeszczuk and Malgorzata Hryniewicka
Journal:
Proc. Amer. Math. Soc. 135 (2007), 23812389
MSC (2000):
Primary 16R20, 16S40, 16W30
Published electronically:
March 29, 2007
MathSciNet review:
2302559
Fulltext PDF Free Access
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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.
If we also assume that is central, then satisfies the standard polynomial identity of degree , where is the greatest integer in .
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 Y. Bahturin, V. Linchenko, Identities of algebras with actions of Hopf algebras, J. Algebra 202 (1998), 634654. MR 1617671 (99d:16040)
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 Y. Bahturin, M. Zaicev, Identities of graded algebras, J. Algebra 205 (1998), 112. MR 1631298 (99f:17034)
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 J. Bergen, M. Cohen, Actions of commutative Hopf algebras, Bull. London Math. Soc., 18 (1986), 159164. MR 0818820 (87e:16052)
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 J. Bergen, M. Cohen, D. Fischman, Irreducible actions and faithful actions of Hopf algebras, Israel J. Math., 72 (1990), 518. MR 1098978 (92g:16044)
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Additional Information
Piotr Grzeszczuk
Affiliation:
Faculty of Computer Science, Technical University of Białystok, Wiejska 45A, 15351 Białystok, Poland
Email:
piotrgr@pb.bialystok.pl
Malgorzata Hryniewicka
Affiliation:
Institute of Mathematics, University of Białystok, Akademicka 2, 15267 Białystok, Poland
Email:
margitt@math.uwb.edu.pl
DOI:
http://dx.doi.org/10.1090/S0002993907087692
PII:
S 00029939(07)087692
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.
