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

Abstract

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

Keywords

• quantum double
• ribbon Hopf algebra
• quasi-triangular Hopf algebra