Duality Theorem and Drinfeld Double in Braided Tensor Categories
Abstract
Let
H
be a finite Hopf algebra with
C
H,H
=
C
−1
H,H
.
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
C
.