Nuclearity of semigroup C*-algebras and the connection to amenability

By Xin Li. 2012

47 citations recorded by the source corpus.

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*-algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full corners in associated group crossed products. These descriptions allow us to characterize nuclearity of semigroup C*-algebras in terms of faithfulness of left regular representations and amenability of group actions. Moreover, we also determine when boundary quotients of semigroup C*-algebras are UCT Kirchberg algebras. This leads to a unified approach to Cuntz algebras and ring C*-algebras.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/23de5b58467157ef9b246624cb84daa75c85b2b1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. S. Echterhoff
2. J. Cuntz
3. Xin Li

In Mathematical Physics

1. Xin Li
2. J. Cuntz
3. S. Echterhoff

Citations in the corpus

• On the K-theory of crossed products by automorphic semigroup actions (2012, methodology): “ to the K-theory of semigroup C*-algebras and semigroup crossed products. We study semigroup crossed products A⋊α,r P in which the semigroup Pacts by automorphisms on the C*-algebra Ain section 4. In [24] it was shown by the third author that, given independence of the set of constructible right ide”