The quantisation of Poisson structures arising in Chern-Simons theory with gauge group G\ltimes \mathfrakg^*

2003/10/31 by C Meusburger, B J Schroers
Physics and Astronomy · Mathematics · #hep-th #gr-qc #math-ph #math.MP

paper · pdf

published as Adv.Theor.Math.Phys. 7 (2004) 1003-1043 · 35 pages, one eps figure; minor corrections

arxiv created 2004/08/27 · arxiv updated 2009/12/01

Abstract

We quantise a Poisson structure on H^n+2g, where H is a semidirect product group of the form G\ltimes\mathfrakg^*. This Poisson structure arises in the combinatorial description of the phase space of Chern-Simons theory with gauge group G\ltimes\mathfrakg^* on R × S_g,n, where S_g,n is a surface of genus g with n punctures. The quantisation of this Poisson structure is a key step in the quantisation of Chern-Simons theory with gauge group G\ltimes\mathfrakg^*. We construct the quantum algebra and its irreducible representations and show that the quantum double D(G) of the group G arises naturally as a symmetry of the quantum algebra.

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