Representation Theory and Noncommutative Geometry, Paris

Cuntz’ K-theoretic amenability revisited

28 janv. 2025, 16:00

1h

Amphitheater Darboux (IHP)

Orateur

Pierre Julg (Université d'Orléans)

Description

In the early 1980’s, the question was raised of comparing the K-theory groups of the full and reduced C*-algebras of a group $G$. J.Cuntz has described a condition (K-amenability) implying that they are isomorphic. Note that K-amenability is incompatible with Kazhdan’s property T, and is implied by the Haagerup property, a strong negation of property T. In this talk we shall explain that Cuntz’ condition relies on the construction of a $G$-Fredhom module. We shall give such a module in the example of ${\mathrm{SL}}_2$ on the fields of $p$-adics (Julg-Valette), of complex numbers (Kasparov) and of real numbers (Fox-Haskel and Julg-Kasparov).