Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type

Abstract

We construct the Grothendieck rings of a class of \mathrm{2}{n}^{\mathrm{2}} dimensional semisimple Hopf Algebras H_{\mathrm{2}{n}^{\mathrm{2}}},which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra H_{\mathrm{8}}.All irreducible H_{\mathrm{2}{n}^{\mathrm{2}}}-modules are classified. Furthermore, we describe the Grothendieck rings r(H_{\mathrm{2}{n}^{\mathrm{2}}}) by generators and relations explicitly.

Key words： Grothendieck ring; Hopf algebra; irreducible module

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