Quantum groups of dimensionpq 2

In this paper we construct two families of non-trivial self-dual semisimple Hopf algebras of dimensionpq ² and investigate closely their (quasi) triangular structures. The paper contains also general results on finite-dimensional triangular Hopf algebras, unimodularity, semisimplicity and ribbon structures of finite-dimensional semisimple Hopf algebras. Dedicated to the memory of Professor S. A. Amitsur This work was partially supported by the Basic Research Foundation administrated by the Israel Academy of Sciences and Humanities. The paper consists of part of the author’s doctoral dissertation written at Ben Gurion University under the supervision of Prof. M. Cohen and Prof. D. E. Radford whom the author wishes to thank for their valuable guidance.