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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Burnside’s theorem for Hopf algebras
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by D. S. Passman and Declan Quinn PDF
Proc. Amer. Math. Soc. 123 (1995), 327-333 Request permission

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
  • © Copyright 1995 American Mathematical Society
  • 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