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Duality Theorems for Infinite Braided Hopf Algebras

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arxiv math/0309007 v6 pith:THQU4OFN submitted 2003-08-31 math.QA math.RA

Shouchuan Zhang , Yanying Han This is my paper · ORCID
classification math.QAmath.RA
keywords braidedalgebrasdualityhopfcategoryinfiniteprovetheorems
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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.

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    The second Lie algebra cohomology of the d-dimensional Witt algebra is computed for all d>2, giving a complete classification of central extensions, and a local universal Grothendieck-Riemann-Roch theorem is proved.

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