Structure of Semisimple Hopf Algebras of Dimension p 2 q 2

Abstract

Let p, q be prime numbers with p 4 < q, and k an algebraically closed field of characteristic 0. We show that semisimple Hopf algebras of dimension p 2 q 2 can be constructed either from group algebras and their duals by means of extensions, or from Radford biproduct R#kG, where kG is the group algebra of group G of order p 2, R is a semisimple Yetter–Drinfeld Hopf algebra in of dimension q 2. As an application, the special case that the structure of semisimple Hopf algebras of dimension 4q 2 is given.