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

 

Burnside's theorem for Hopf algebras


Authors: D. S. Passman and Declan Quinn
Journal: Proc. Amer. Math. Soc. 123 (1995), 327-333
MSC: Primary 16W30; Secondary 16S30, 16S34
MathSciNet review: 1215204
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Abstract: A classical theorem of Burnside asserts that if $ \chi $ is a faithful complex character for the finite group G, then every irreducible character of G is a constituent of some power $ {\chi ^n}$ of $ \chi $. Fifty years after this appeared, Steinberg generalized it to a result on semigroup algebras $ K[G]$ with K an arbitrary field and with G a semigroup, finite or infinite. Five years later, Rieffel showed that the theorem really concerns bialgebras and Hopf algebras. In this note, we simplify and amplify the latter work.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1215204-6
PII: S 0002-9939(1995)1215204-6
Article copyright: © Copyright 1995 American Mathematical Society