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

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

2008-04-28

arxiv.org/abs/0804.4454v1

Mathematics

K-Theory and Homology

29 pages, in french

Scientific paper

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].

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