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 -