Quasitriangular structures for a class of Hopf algebras of dimension p6

We study quasitriangular structur s in the A star H which is the twisted smash product Hopf algebra. As an application, we consider a class of non-commutative and non-cocommutative Hopf algebras H-p(alpha, beta, q, m) which are pointed non semisimple, and establish quasitriangular structures on H-p(alpha, beta, q, m). Another objective of this paper is to study the ling extensions A(1)(biH) subset of A subset of A star H. W prove a Maschke-type theorem for an A star H-modules. We form a associated Morita context [A(biH), A, A, A star H] and use these to investigate s o*me of properties of the Doi-Takeuchi double and the Drinfeld's double.