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The Representation Ring of the Twisted Quantum Double of a Finite Group

Published online by Cambridge University Press:  20 November 2018

S. J. Witherspoon
S. J. Witherspoon*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 3G3 e-mail: sjw@math.toronto.edu
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Abstract

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We provide an isomorphism between the Grothendieck ring of modules of the twisted quantum double of a finite group, and a product of centres of twisted group algebras of centralizer subgroups. It follows that this Grothendieck ring is semisimple. Another consequence is a formula for the characters of this ring in terms of representations of twisted group algebras of centralizer subgroups.

Keywords

16G3016S3516W3020C25finite groupHopf algebraquasi-Hopf algebraquantum doublerepresentation ringGrothendieck ringtwisted group algebra
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 6 , 01 December 1996 , pp. 1324 - 1338
Copyright
Copyright © Canadian Mathematical Society 1996

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