On oriented quantum algebras derived from representations of the quantum double of a finite-dimensional Hopf algebra

Let H be a finite-dimensional Hopf algebra over a field k. We study the simple left modules M of the Drinfelʹd double D(H) and characterize them when H is graded with commutative cocommutative bottom term. In the special case when H is a Taft (Hopf ) algebra or a close relative, we calculate the character of M and give an explicit description of oriented quantum algebra structures on End(M) related to a very natural oriented quantum algebra structure on D(H). The R-matrices associated with End(M) are spin preserving.