Duality Theorems for Infinite Braided Hopf Algebras

Details Duality Theorems for Infinite Braided Hopf Algebras Duality Theorems for Infinite Braided Hopf Algebras

2003-08-31

arxiv.org/abs/math/0309007v6

Mathematics

Quantum Algebra

11pages

Scientific paper

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.

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