Kolloquium des Departments Mathematik

Jun 25
25. June 2019 16:30 - 17:30
HS H13

C*-algebras associated to semigroups and number fields

Referent: Prof. Dr. Siegfried Echterhoff, Universität Münster
Veranstalter: Hermann Schulz-Baldes

To many mathematical objects one can naturally associate C*-algebras which reflect important properties of the underlying objects. In this lecture we study C*-algebras associated to semigroups. We show that in many important cases there are nice formulas for the computation of the K-theory groups of these algebras. This applies in particular for the multiplicative semi group $R^\times$ and the $ax+b$-semigroup $R\rtimes R^{\times}$ of the ring of integers $R$ in a number field $K$, and it turns out that the $K$-theory groups of the associated $C^*$-algebras are strongly connected to the ideal class groups of the ring $R$.

This lecture is based on joint work with Joachim Cuntz and Xin Li.