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The Representation Ring and the Centre of a Hopf Algebra

Published online by Cambridge University Press:  20 November 2018

Sarah J. Witherspoon
Sarah J. Witherspoon*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 3G3 email: sjw@math.toronto.edu,
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Abstract

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When $H$ is a finite dimensional, semisimple, almost cocommutative Hopf algebra, we examine a table of characters which extends the notion of the character table for a finite group. We obtain a formula for the structure constants of the representation ring in terms of values in the character table, and give the example of the quantum double of a finite group. We give a basis of the centre of $H$ which generalizes the conjugacy class sums of a finite group, and express the class equation of $H$ in terms of this basis. We show that the representation ring and the centre of $H$ are dual character algebras (or signed hypergroups).

Keywords

16W3020N20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 4 , 01 August 1999 , pp. 881 - 896
Copyright
Copyright © Canadian Mathematical Society 1999

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