The Representation Ring and the Centre of a Hopf Algebra

http://dx.doi.org/10.4153/CJM-1999-038-5
Canad. J. Math. 51(1999), 881-896

  Published:1999-08-01
 Printed: Aug 1999

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).