Mapping class group actions in Chern - Simons theory with gauge group G ⋉ g ∗
نویسنده
چکیده
We study the action of the mapping class group of an oriented genus g surface Sg,n with n punctures on a Poisson algebra which arises in the combinatorial description of Chern-Simons gauge theory on R × Sg,n when the gauge group is a semidirect product G ⋉ g . 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 braid group via its universal R-matrix.
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