Prof. Dr. Søren Eilers, Universität Kopenhagen
The complete classification of Cuntz-Krieger algebras
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 K0-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.