Representations of matched pairs of groupoids and applications to weak Hopf algebras

Details Representations of matched pairs of groupoids and applications to weak Hopf algebras Representations of matched pairs of groupoids and applications to weak Hopf algebras

2004-02-07

arxiv.org/abs/math/0402118v1

Contemp. Math. 376 (2005), 127-173.

Mathematics

Quantum Algebra

Scientific paper

We introduce the category of set-theoretic representations of a matched pair of groupoids. This is a monoidal category endowed with a monoidal functor to the category of quivers over the common base of the groupoids in the matched pair (the forgetful functor). We study monoidal functors between two such categories of representations which preserve the forgetful functor. We show that the centralizer of such a monoidal functor is the category of representations of a new matched pair, which we construct explicitly. We introduce the notions of {\em double} of a matched pair of groupoids and {\em generalized double} of a morphism of matched pairs. We show that the centralizer of the forgetful functor is the category of representations of the dual matched pair, and the centralizer of the identity functor (the center) is the category of representations of the double. We use these constructions to classify the braidings in the category of representations of a matched pair. Such braidings are parametrized by certain groupoid-theoretic structures which we call {\em matched pairs of rotations}. Finally, we express our results in terms of the weak Hopf algebra associated to a matched pair of groupoids. A matched pairs of rotations gives rise to a quasitriangular structure for the associated weak Hopf algebra. The Drinfeld double of the weak Hopf algebra of a matched pair is the weak Hopf algebra associated to the double matched pair.

Affiliated with

Also associated with

No associations

Rating

Representations of matched pairs of groupoids and applications to weak Hopf algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Representations of matched pairs of groupoids and applications to weak Hopf algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations of matched pairs of groupoids and applications to weak Hopf algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-66159