Grothendieck Rings of 2$n^2$ dimensional Hopf Algebras $H_{2n^2}$

Abstract

In this paper, we construct the Grothendieck ring of a class of 2n 2 -dimension semisimple Hopf Algebras H 2n 2 , which can be viewed as a generalization of the 8dimension Kac-Paljutkin Hopf algebra K8. All irreducible H 2n 2 -modules are classified. Furthermore, we describe the Grothendieck ring r(H 2n 2 ) by generators and relations explicitly.