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

Let s, t be two positive integers and k be an algebraically closed field with char ( k) ∤ s t . We show that the Drinfeld double D (⋀ s t , t * c o p) of generalized Taft–Hopf algebra ⋀ s t , t * c o p has ribbon elements if and only if t is odd. Moreover, if s is even and t is odd, then D (⋀ s t , t * c o p) has two ribbon elements, and if both s and t are odd, then D (⋀ s t , t * c o p) has only one ribbon element. Finally, we compute explicitly all ribbon elements of D (⋀ s t , t * c o p) . [ABSTRACT FROM AUTHOR]