Cosemisimple Hopf algebras with antipode of arbitrary finite order

Abstract:

Let $m \geq 1$ be a positive integer. We show that, over an algebraically closed field of characteristic zero, there exist cosemisimple Hopf algebras having an antipode of order $2m$. We also discuss the Schur indicator for such Hopf algebras.

Laboratoire de Math\'ematiques Appliqu\'ees, Universit\'e de Pau et des Pays de l'Adour, IPRA, Avenue de l'universit\'e, 64000 Pau, France.
Julien.Bichon@univ-pau.fr