Mapping class group actions in Chern-Simons theory with gauge group G ⋉ g*

Meusburger C, Schroers B (2005)


Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2005

Journal

Publisher: Elsevier

Book Volume: 706

Pages Range: 569-597

Journal Issue: 3

DOI: 10.1016/j.nuclphysb.2004.10.057

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 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 exchange of punctures via its universal R-matrix. © 2004 Elsevier B.V. All rights reserved.

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APA:

Meusburger, C., & Schroers, B. (2005). Mapping class group actions in Chern-Simons theory with gauge group G ⋉ g*. Nuclear Physics B, 706(3), 569-597. https://dx.doi.org/10.1016/j.nuclphysb.2004.10.057

MLA:

Meusburger, Cathérine, and Bernd Schroers. "Mapping class group actions in Chern-Simons theory with gauge group G ⋉ g*." Nuclear Physics B 706.3 (2005): 569-597.

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