Burnside’s theorem for Hopf algebras

Passman, D. S.; Quinn, Declan

doi:10.1090/S0002-9939-1995-1215204-6

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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