### Abstract

In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions, the phase space is the moduli space of flat G-connections on a two-dimensional surface, 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 quantization of that Poisson structure.

Original language | English |
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Title of host publication | Quantization of Singular Symplectic Quotients |

Editors | N. P. Landsman, M. Pflaum, M. Schlichenmaier |

Publisher | Birkhäuser |

Pages | 307-327 |

Number of pages | 21 |

ISBN (Electronic) | 978-3-0348-8364-1 |

ISBN (Print) | 978-3-0348-9535-4 |

DOIs | |

Publication status | Published - 2001 |

Event | Workshop on Quantization of Singular Symplectic Quotients 1999 - Oberwolfach, Germany Duration: 2 Aug 1999 → 6 Aug 1999 |

### Publication series

Name | Progress in Mathematics |
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Publisher | Birkhäuser Basel |

Volume | 198 |

ISSN (Print) | 0743-1643 |

### Conference

Conference | Workshop on Quantization of Singular Symplectic Quotients 1999 |
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Country | Germany |

City | Oberwolfach |

Period | 2/08/99 → 6/08/99 |

### Keywords

- CHERN-SIMONS THEORY
- QUANTUM

## Cite this

Schroers, B. J. (2001). Combinatorial quantization of Euclidean gravity in three dimensions. In N. P. Landsman, M. Pflaum, & M. Schlichenmaier (Eds.),

*Quantization of Singular Symplectic Quotients*(pp. 307-327). (Progress in Mathematics; Vol. 198). Birkhäuser. https://doi.org/10.1007/978-3-0348-8364-1_12