Ribbon Hopf Superalgebras and Drinfel'd Double

Finite dimensional ribbon Hopf (super) algebras play an important role in constructing invariants of 3-manifolds. In the present paper, the authors give a necessary and sufficient condition for the Drinfel’d double of a finite dimensional Hopf superalgebra to have a ribbon element. The criterion can be seen as a generalization of Kauffman and Radford’s result in the non-super situation to the ?₂-graded situation, however, the derivation of the result in the ?₂-graded case will be much more complicated.