The character table for a Hopf algebra arising from the Drinfel'd double.
The main result of this paper is the construction of a character table for a Hopf algebra \(H\) with bijective antipode over a field of characteristic zero. This construction involves two natural actions of the Drinfeld double \(D(H)\) on \(H\). When \(H\) is (finite dimensional) semisimple, a formula for the character table is given, generalizing the formulas for character tables of finite groups. The example where \(H\) is the Kac-Paljutkin semisimple Hopf algebra of dimension 8 is studied. Related previous work appears in the author's paper [Bull. Sci. Math. 125, No. 4, 279-296 (2001; Zbl 1007.16030)].
scientific article; zbMATH DE number 1963604