Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10721441 | Nuclear Physics B | 2005 | 29 Pages |
Abstract
We study the action of the mapping class group of an oriented genus g surface with n punctures and a disc removed on a Poisson algebra which arises in the combinatorial description of Chern-Simons gauge theory when the gauge group is a semidirect product Gâg*. We prove that the mapping class group acts on this algebra via Poisson isomorphisms and express the action of Dehn twists in terms of an infinitesimally generated G-action. We construct a mapping class group representation on the representation spaces of the associated quantum algebra and show that Dehn twists can be implemented via the ribbon element of the quantum double D(G) and the exchange of punctures via its universal R-matrix.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
C. Meusburger, B.J. Schroers,