Duality Theorem and Drinfeld Double in Braided Tensor Categories

Details Duality Theorem and Drinfeld Double in Braided Tensor Categories Duality Theorem and Drinfeld Double in Braided Tensor Categories

2003-07-17

arxiv.org/abs/math/0307255v2

Algebra Colloq. 10(2003)2, 127--134

Mathematics

Rings and Algebras

8. to appear in Algebra Colloquium

Scientific paper

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 ${\cal
C}$.

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