Operator Algebra seminar

Speaker: Christian Voigt (University of Glasgow)

Title: A deformation of the Baum-Connes assembly map

Abstract: A central theme in the study of K-theory of operator algebras is the Baum-Connes conjecture, which predicts the K-theory of group C*-algebras and crossed products. In the case of complex semisimple Lie groups like SL(n, C), the conjecture asserts that a certain deformation induces an isomorphism in K-theory. In this talk I’ll first review this construction, and then explain a similar picture for complex semisimple quantum groups. These quantum groups can be viewed as deformations of classical complex semisimple groups; technically they are obtained using the Drinfeld double construction. In particular, I’ll show how to obtain an analogue of the Baum-Connes assembly map in this setting. The quantum assembly map is an isomorphism, and it contains the classical Baum-Connes assembly map as a direct summand. I’ll also discuss how the various deformations involved fit together on a conceptual level.