### 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.

Original language | English |
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Pages (from-to) | 569-597 |

Number of pages | 29 |

Journal | Nuclear Physics B |

Volume | 706 |

Issue number | 3 |

DOIs | |

Publication status | Published - 7 Feb 2005 |

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## Cite this

*Nuclear Physics B*,

*706*(3), 569-597. https://doi.org/10.1016/j.nuclphysb.2004.10.057