Traces and reduced group C∗ -algebras

Indira Chatterji (1) , Guido Mislin (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

We study the universal (Hattori-Stallings) trace on the K-theory of Banach algebras containing the complex group ring. As a result, we prove that for a group satisfying the Baum-Connes conjecture, finitely generated projectives over the reduced group C*-algebra satisfy a condition reminiscent of the Bass conjecture. An immediate consequence is that in the torsion-free case, the change of ring map from the reduced group C*-algebra to the von Neumann algebra of the group induces the zero map at the level of reduced K-theory.

Domaines: K-théorie et homologie [math.KT]

Indira Chatterji, Guido Mislin. Traces and reduced group C∗ -algebras. Contemporary mathematics, 2006, 209, pp.73. ⟨hal-00472045⟩