BURNSIDES THEOREM FOR HOPF-ALGEBRAS

A classical theorem of Burnside asserts that if chi is a faithful comp lex 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 algeb ras K[G] with K an arbitrary field and with G a semigroup, finite or i nfinite. Five years later, Rieffel showed that the theorem really conc erns bialgebras and Hopf algebras. In this note, we simplify and ampli fy the latter work.