Abstract:

Analyzing the order of the group consisting of group\|like elements of a semisimple Hopf algebra, the authors obtained the structures of semisimple Hopf algebras of dimension pq³ over an algebraically closed field of characteristic 0: they are either semisolvable, or isomorphic to a Radford biproduR#A, where p,q are prime numbers to meet the needs of  p>q ², A is a semisimple Hopf algebra of dimension q ³, R is a semisimple Yetter-Drinfeld Hopf algebra in of dimension p.

Key words: semisimple Hopf algebra, semisolvability, Radford biproduct, character, Drinfeld double