BURNSIDES THEOREM FOR HOPF-ALGEBRAS

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.