TY - JOUR

T1 - Burnside's theorem for hopf algebras

AU - Passman, D. S.

AU - Quinn, Declan

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

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.

UR - http://www.scopus.com/inward/record.url?scp=84966244224&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966244224&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1995-1215204-6

DO - 10.1090/S0002-9939-1995-1215204-6

M3 - Article

AN - SCOPUS:84966244224

VL - 123

SP - 327

EP - 333

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -