Factorization of simple modules for certain pointed Hopf algebras

We study the representations of two types of pointed Hopf algebras: restricted two-parameter quantum groups, and the Drinfel'd doubles of rank one pointed Hopf algebras of nilpotent type. We study, in particular, under what conditions a simple module can be factored as the tensor product of a one dimensional module with a module that is naturally a module for the quotient by central group-like elements.