Topological invariants from non-restricted quantum groups

Details Topological invariants from non-restricted quantum groups Topological invariants from non-restricted quantum groups

2010-09-21

arxiv.org/abs/1009.4120v1

Mathematics

Geometric Topology

37 pages, 16 figures

Scientific paper

We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in arXiv:1008.3103 and arXiv:0910.1624, respectively. In this case we show that these invariants are equal and extend to what we call a relative Homotopy Quantum Field Theory which is a branch of the Topological Quantum Field Theory founded by E. Witten and M. Atiyah. Our main examples of relative spherical categories are the categories of finite dimensional weight modules over non-restricted quantum groups considered by C. De Concini, V. Kac, C. Procesi, N. Reshetikhin and M. Rosso. These categories are not semi-simple and have an infinite number of non-isomorphic irreducible modules all having vanishing quantum dimensions. We also show that these categories have associated ribbon categories which gives rise to re-normalized link invariants. In the case of sl(2) these link invariants are the Alexander-type multivariable invariants defined by Y. Akutsu, T. Deguchi, and T. Ohtsuki.

Affiliated with

Also associated with

No associations

Rating

Topological invariants from non-restricted quantum groups 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 Topological invariants from non-restricted quantum groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological invariants from non-restricted quantum groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-697674