arXiv subjects

Maria-Paula Gomez-Aparicio

Publications and source records attributed to Maria-Paula Gomez-Aparicio.

3 recordsLinked to original sources

arXiv2008

Non-unitary representations, Baum-Connes morphism and unconditional completions

We show that the Baum-Connes morphism twisted by a non-unitary representation, defined in [GA08], is an isomorphism for a large class of groups satisfying the Baum-Connes conjecture. Such class contains all the real semi-simple Lie groups, all hyperbolic groups and many infinite discret groups having Kazhdan's property (T). We define a tensorisation by a non-unitary finite dimensional representation on the left handside of the Baum-Connes morphism and we show that its analogue in K-theory must be defined on the K-theory of the twisted group algebras introduced in [GA07b].

math.KT↗

arXiv2008

Twisting the Baum-Connes morphism by a non-unitary representation

Let G be a locally compact group and rho a non-unitary finite dimensional representation of G. We consider tensor products of rho by some unitary representations of G in order to define two Banach algebras analogous to the group C*-algebras, C*(G) and C*_r(G). We calculate the K-theory of such algebras for a large class of groups satisfying the Baum-Connes conjecture.

math.OA↗

arXiv2007

Sur la Propriété (T) tordue par un produit tensoriel

In this article, we consider tensor products of unitary representations by irreducible non-unitary finite dimensional representations of topological groups to define a property that is a twisting of Kazhdan's Property (T). We use the uniform decay of the matrix coefficients of unitary representations, to show that for most of the real semi-simple Lie groups having Kazhdan's Property (T), any finite dimensional irreducible representation $ρ$ of $G$, is isolated among representations of the form $ρ\otimesπ$, where $π$ ranges over the irreducible unitary representations, in a sense to be made precise.

math.RT↗