## 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