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December, 2003 The quantisation of Poisson structures arising in Chern-Simons theory with gauge group $G \ltimes \mathfrak{g}^*$
C. Meusburger, B. J. Schroers
Adv. Theor. Math. Phys. 7(6): 1003-1043 (December, 2003).

Abstract

We quantise a Poisson structure on $H^{n+2g}$, where $H$ is a semidirect product group of the form $G\ltimes\mathfrak{g}^*$. This Poisson structure arises in the combinatorial description of the phase space of Chern-Simons theory with gauge group $G\ltimes\mathfrak{g}^*$ on $\mathbb{R}\times S_{g,n}$, 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 $G\ltimes\mathfrak{g}^*$. 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.

Citation

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C. Meusburger. B. J. Schroers. "The quantisation of Poisson structures arising in Chern-Simons theory with gauge group $G \ltimes \mathfrak{g}^*$." Adv. Theor. Math. Phys. 7 (6) 1003 - 1043, December, 2003.

Information

Published: December, 2003
First available in Project Euclid: 21 June 2004

zbMATH: 1063.81078
MathSciNet: MR2061642

Rights: Copyright © 2003 International Press of Boston

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Vol.7 • No. 6 • December, 2003
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