# Propriété (T) et morphisme de Baum-Connes tordus par une représentation non unitaire

Abstract : My thesis concerns some twistings of Kazhdan's property (T) and the Baum-Connes morphism by a non-unitary representation. In Chapter 1, given a locally compact group G and a non-unitary finite dimensional representation rho of G, we consider tensor products of rho by some unitary representations of G to define two twisted Banach group algebras, Amax(rho) et A(rho), analoguous to the group C*-algebras, C*(G) and C*r(G). We then defined a twisting of property (T) in terms of Amax(rho) and we showed that most of the real semi-simple Lie groups having property (T) have twisted property (T) for all irreducible finite dimensional representations rho.
In Chapter 2 and 3 we have calculated the K-theory of these twisted Banach algebras for a large class of groups satisfying the Baum-Connes conjecture. To do so, we have defined a twisted Baum-Connes morphism with image in the K-theory of the twisted algebras, and we have showed that it is an isomorphism in almost all the cases in which we know the Baum-Connes coonjecture is true.
In Chapter 4, we have showed that an analoguous in K-theory to the action induced by the tensor product of a finite dimensional representation on the left handside of the Baum-Connes map, has to be defined on the K-theory of the twisted Banach group algebras.
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Cited literature [61 references]

https://tel.archives-ouvertes.fr/tel-00274378
Contributor : Maria Paula Gomez Aparicio <>
Submitted on : Friday, April 18, 2008 - 11:20:09 AM
Last modification on : Wednesday, December 9, 2020 - 3:16:51 PM
Long-term archiving on: : Friday, September 28, 2012 - 12:47:26 PM

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• HAL Id : tel-00274378, version 1

### Citation

Maria Paula Gomez Aparicio. Propriété (T) et morphisme de Baum-Connes tordus par une représentation non unitaire. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2007. Français. ⟨tel-00274378⟩

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