Ribbon Hopf Superalgebras and Drinfel’d Double

The Ribbon Elements of the Quantum Double of Generalized Taft–Hopf Algebra

“…Thus, researchers have paid much attention to the question of when a quasi-triangular Hopf algebra has ribbon structures. In [3], Chen and Yang gave a necessary and sufficient condition for the Drinfeld double of a finitedimensional Hopf superalgebra to have a ribbon element. Kauffman and Radford [4] gave a necessary and sufficient condition for the Drinfeld double of a finite-dimensional Hopf algebra to admit a ribbon structure, and they proved that (D(A n (q)), R) is a ribbon Hopf algebra if and only if n is odd, where D(A n (q)) is the Drinfeld double of n 2 -dimensional Taft algebra A n (q) and R is the universal R-matrix of D(A n (q)).…”