TY - JOUR
T1 - Burnside's theorem for hopf algebras
AU - Passman, D. S.
AU - Quinn, Declan
PY - 1995/2
Y1 - 1995/2
N2 - 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 xx 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.
AB - 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 xx 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.
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U2 - 10.1090/S0002-9939-1995-1215204-6
DO - 10.1090/S0002-9939-1995-1215204-6
M3 - Article
AN - SCOPUS:84966244224
SN - 0002-9939
VL - 123
SP - 327
EP - 333
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 2
ER -