### 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 x^{x} of X 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.

Original language | English (US) |
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Pages (from-to) | 327-333 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 123 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1995 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Passman, D. S., & Quinn, D. (1995). Burnside's theorem for hopf algebras.

*Proceedings of the American Mathematical Society*,*123*(2), 327-333. https://doi.org/10.1090/S0002-9939-1995-1215204-6