## Abstract

We continue studying properties of semisimple Hopf algebras H over algebraically closed fields of characteristic 0 resulting from their generalized character tables. We show that the generalized character table of H reflects normal left coideal subalgebras of H. These are the Hopf analogues of normal subgroups in the sense that they arise from Hopf quotients. We apply these ideas to prove Hopf analogues of known results in group theory. Among the rest we prove that columns of the character table are orthogonal and that all entries are algebraic integers. We analyze 'semi-kernels' and their relations to the character table. We prove a full analogue of the Burnside-Brauer theorem for almost cocommutative H. We also prove the Hopf algebras analogue of the following (Burnside) theorem: If G is a non-abelian simple group then {1} is the only conjugacy class of G which has prime power order.

Original language | English |
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Pages (from-to) | 1845-1866 |

Number of pages | 22 |

Journal | Journal of Pure and Applied Algebra |

Volume | 218 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2014 |

### Bibliographical note

Funding Information:This research was supported by the ISRAEL SCIENCE FOUNDATION , 170-12 .

### Funding

This research was supported by the ISRAEL SCIENCE FOUNDATION , 170-12 .

Funders | Funder number |
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Israel Science Foundation | 170-12 |