## Abstract

Let H be a semisimple Hopf algebras over an algebraically closed field k of characteristic 0. We define Hopf algebraic analogues of commutators and their generalizations and show how they are related to ^{H '}, the Hopf algebraic analogue of the commutator subgroup. We introduce a family of central elements of ^{H '}, which on one hand generate ^{H '} and on the other hand give rise to a family of functionals on H. When H = k G, G a finite group, these functionals are counting functions on G. It is not clear yet to what extent they measure any specific invariant of the Hopf algebra. However, when H is quasitriangular they are at least characters on H.

Original language | English |
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Pages (from-to) | 111-130 |

Number of pages | 20 |

Journal | Journal of Algebra |

Volume | 398 |

DOIs | |

State | Published - 15 Jan 2014 |

### Bibliographical note

Funding Information:This research was supported by the Israel Science Foundation , 170-12 .

## Keywords

- Commutator algebra
- Commutators
- Conjugacy classes
- Counting functions
- Generalized commutators
- Iterated commutators
- Normalized class sums