Paths on graphs and associated quantum groupoids

Details Paths on graphs and associated quantum groupoids Paths on graphs and associated quantum groupoids

2010-04-28

arxiv.org/abs/1004.5104v4

Mathematics

Quantum Algebra

To appear in the proceedings of "Colloquium on Hopf Algebras, Quantum Groups and Tensor Categories", August 31st to September

Scientific paper

Given any simple biorientable graph it is shown that there exists a weak {*}-Hopf algebra constructed on the vector space of graded endomorphisms of essential paths on the graph. This construction is based on a direct sum decomposition of the space of paths into orthogonal subspaces one of which is the space of essential paths. Two simple examples are worked out with certain detail, the ADE graph $A_{3}$ and the affine graph $A_{[2]}$. For the first example the weak {*}-Hopf algebra coincides with the so called double triangle algebra. No use is made of Ocneanu's cell calculus.

Affiliated with

Also associated with

No associations

Rating

Paths on graphs and associated quantum groupoids 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 Paths on graphs and associated quantum groupoids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Paths on graphs and associated quantum groupoids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-69378