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

DOI:
https://doi.org/10.1090/S0002-9939-1995-1215204-6

MathSciNet review:
1215204

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Abstract | References | Similar Articles | Additional Information

Abstract: A classical theorem of Burnside asserts that if is a faithful complex character for the finite group *G*, then every irreducible character of *G* is a constituent of some power of . Fifty years after this appeared, Steinberg generalized it to a result on semigroup algebras 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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DOI:
https://doi.org/10.1090/S0002-9939-1995-1215204-6

Article copyright:
© Copyright 1995
American Mathematical Society