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Combinatorial quantisation of Euclidean gravity in three dimensions

Bernd J Schroers
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Abstract

In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat G-connections, where G is a typically non-compact Lie group which depends on the signature of space-time and the cosmological constant. For Euclidean signature and vanishing cosmological constant, G is the three-dimensional Euclidean group. For this case the Poisson structure of the moduli space is given explicitly in terms of a classical r-matrix. It is shown that the quantum R-matrix of the quantum double D(SU(2)) provides a quantisation of that Poisson structure.

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Bernd J Schroers. 2000-07-03. Combinatorial quantisation of Euclidean gravity in three dimensions. https://arxiv.org/abs/math/0006228

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