Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity

Details Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity

1994-05-26

arxiv.org/abs/hep-th/9405167v2

Commun.Math.Phys. 172 (1995) 467-516

Physics

High Energy Physics

High Energy Physics - Theory

61 pages, 12 eps figures. Hennings' invariant is a particular case of the described invariant; references added

Scientific paper

10.1007/BF02101805

An example of a finite dimensional factorizable ribbon Hopf C-algebra is given by a quotient H=u_q(g) of the quantized universal enveloping algebra U_q(g) at a root of unity q of odd degree. The mapping class group M_{g,1} of a surface of genus g with one hole projectively acts by automorphisms in the H-module H^{*\otimes g}, if H^* is endowed with the coadjoint H-module structure. There exists a projective representation of the mapping class group M_{g,n} of a surface of genus g with n holes labelled by finite dimensional H-modules X_1,...,X_n in the vector space Hom_H(X_1\otimes...\otimes X_n,H^{*\otimes g}). An invariant of closed oriented 3-manifolds is constructed. Modifications of these constructions for a class of ribbon Hopf algebras satisfying weaker conditions than factorizability (including most of u_q(g) at roots of unity q of even degree) are described. The results are motivated by CFT.

Affiliated with

Also associated with

No associations

Rating

Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity 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 Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-398495