## Abstract

We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sums up to d ^{-2} where d = dim H. We show also that in this case the character table is obtained from the S-matrix associated to D(H). Finally, we calculate explicitly the generalized character table of D(kS _{3}, which is not a character table for any group. It moreover provides an example of a product of two class sums which is not an integral combination of class sums.

Original language | English |
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Pages (from-to) | 4618-4633 |

Number of pages | 16 |

Journal | Communications in Algebra |

Volume | 39 |

Issue number | 12 |

DOIs | |

State | Published - 1 Dec 2011 |

## Keywords

- Character algebras
- Character table
- Class sums
- Conjugacy classes
- S-matrix
- Semisimple Hopf algebras

## ASJC Scopus subject areas

- Algebra and Number Theory