The Grothendieck ring of Yetter-Drinfeld modules over a class of 2n 2-dimensional Kac-Paljutkin Hopf algebras

Abstract

As is well known, a class of -dimensional Kac-Paljutkin Hopf algebras was introduced by Pansera. It is the generalization of the 8-dimensional Kac-Paljutkin Hopf algebra H 8. In this paper, the classification of Yetter-Drinfeld modules over is given by Radford’s method of constructing Yetter-Drinfeld modules for a Hopf algebra. Furthermore, the tensor product of Yetter-Drinfeld modules over is established, and the Grothendieck ring is described explicitly by generators and relations. Communicated by Julia Plavnik