Mathematische Gesellschaft

Donnerstag, 26.05.2016

Prof. Dr. Søren Eilers, Universität Kopenhagen

The complete classification of Cuntz-Krieger algebras

Abstract:

In 1980, Jochaim Cuntz and Wolfgang Krieger showed how to associate a functional analytic object, more precisely a C^{*}-algebra, to any finite graph with no stranded vertices in a way reflecting the dynamics of the shift space associated to such a graph, and from the early days of the classification theory of C^{*}-algebras this class was under scrutiny to establish classification results by *K*-theory.

Indeed, Mikael Rørdam in 1955 completed the of those
Cuntz-Krieger algebras that are simple, by employing in a
groundbreaking way that the *K*^{0}-group of such a C^{*}-algebra is precisely the Bowen-Franks group well-known in the classification of shift spaces.

I will report on how recent understanding of the larger class of graph
C^{*}-algebra has recently allowed for a complete solution of the classification problem for Cuntz-Krieger algebras in a way which is
not directly reflected in the dynamics. The part of the work which I
have contributed is joint with Restorff, Ruiz and Sørensen.