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KK-théorie équivariante et opérateur de Julg-Valette pour les groupes quantiques

Abstract : This thesis deals with the study of the equivariant KK-theory with respect to locally compact quantum groups. We generalize well-known notions and results of the classical case: stabilisation theorem, descent morphisms, Green-Julg theorem, K-amenability. Then, we try to introduce useful geometric tools in this setting. In particular, we associate to any discrete quantum group, and to any amalgamated free product of discrete quantum groups, objects that can be interpreted as quantum trees. We study in detail the Julg-Valette operators that are associated to the Wang-Banica free quantum groups: they present many new features characteristic of the quantum frame, the most important one being the non-involutivity of the direction reversing operator on the space of oriented edges. It makes necessary the introduction of a new representation of the discrete quantum group in order to obtain a KK-theory element.
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Contributor : Roland Vergnioux <>
Submitted on : Thursday, February 20, 2003 - 6:49:46 PM
Last modification on : Tuesday, December 1, 2020 - 2:34:03 PM
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  • HAL Id : tel-00001809, version 1



Roland Vergnioux. KK-théorie équivariante et opérateur de Julg-Valette pour les groupes quantiques. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2002. Français. ⟨tel-00001809⟩



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