Duality Theorem and Drinfeld Double in Braided Tensor Categories

2003/07/31 by Shouchuan Zhang
Mathematics · #math.RA #msc:16w30

paper · pdf

published as Algebra Colloq. 10(2003)2, 127--134 · 8. to appear in Algebra Colloquium

arxiv created 2004/12/12 · arxiv updated 2009/12/01

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 ^* ≅ R ⊗ (H ⊗ H ^*) \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.

Related

• Duality Theorems for Infinite Braided Hopf Algebras
• Duality Theorem and Hom Functor in Braided Tensor Categories
• The doubles of a braided Hopf algebra
• Yetter-Drinfeld categories for quasi-Hopf algebras
• More properties of Yetter-Drinfeld category over dual quasi-Hopf algebras