# On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup

### Joachim Cuntz

Universität Münster, Germany### Siegfried Echterhoff

Universität Münster, Germany### Xin Li

Queen Mary University of London, United Kingdom

## Abstract

We compute the K-theory of C*-algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the K-theory of these semigroup C*-algebras in terms of the K-theory for the reduced group C*-algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.

## Cite this article

Joachim Cuntz, Siegfried Echterhoff, Xin Li, On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup. J. Eur. Math. Soc. 17 (2015), no. 3, pp. 645–687

DOI 10.4171/JEMS/513