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Exemples et applications des groupoïdes quantiques finis

Abstract : In this thesis, we construct a concrete family of inclusions of type II_1 factors with index (n+sqrt( n))^2 , for n natural greater or equal to 1, and we study their intermediate factors, in particular their indices and principal graphs. We use actions of weak Hopf C*-algebras on the hyperfinite type II_1 factors and then the Galois correspondence between intermediate factors and coidalgebras. First, we describe a family of weak Hopf C*-algebras obtained by application of the reconstruction theorem for fusion categories to Tambara-Yamagami categories. We give two families of coidalgebras and show they form a lattice. We can then construct the inclusions of factors and some intermediate factors. Second, we make the link between coidalgebras and module categories and we describe a certain type of module categories over Tambara-Yamagami categories. This classification is complete for a subfamily of Tambara-Yamagami categories and this leads to an exhaustive description of principal graphs of intermediate factors.
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Contributor : Camille Mével <>
Submitted on : Thursday, July 8, 2010 - 6:24:03 PM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM
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  • HAL Id : tel-00498884, version 1


Camille Mével. Exemples et applications des groupoïdes quantiques finis. Mathématiques [math]. Université de Caen, 2010. Français. ⟨tel-00498884⟩



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