Duality Theorems for Infinite Braided Hopf Algebras

Abstract

Let $H$ be an infinite-dimensional braided Hopf algebra and assume that the braiding is symmetric on $H$ and its quasi-dual $H^d$. We prove the Blattner-Montgomery duality theorem, namely we prove $$ (R # H)# H^{d} \cong R \otimes (H # H^{d}) \hbox {as algebras in braided tensor category} {\cal C}.$$ In particular, we present two duality theorems for infinite braided Hopf algebras in the Yetter-Drinfeld module category.

11pages

References in corpus (4)

• Vertex operator algebras, the Verlinde conjecture and modular tensor categories
• Algebras and Hopf Algebras in Braided Categories
• Open-string vertex algebras, tensor categories and operads
• Duality Theorem and Drinfeld Double in Braided Tensor Categories

Cited by in corpus (1)

• Duality Theorem and Hom Functor in Braided Tensor Categories