Duality Theorem and Drinfeld Double in Braided Tensor Categories

Abstract

Let $H$ be a finite Hopf algebra with $C_{H,H}=C_{H,H}^{-1}.$ The duality theorem is shown for $H$, i.e., $$ (R # H)# H^{\hat *} \cong R \otimes (H \bar \otimes H^{\hat *}) \hbox {as algebras in} {\cal C}.$$ Also, it is proved that the Drinfeld double $(D(H),[b])$ is a quasi-triangular Hopf algebra in $\mathcal{C}$.

8. to appear in Algebra Colloquium

Cited by in corpus (1)

• Hopf Galois Extension in Braided Tensor Categories