Li, X. (2013) Nuclearity of semigroup C*-algebras and the connection to amenability. Advances in Mathematics, 244, pp. 626-662. (doi: 10.1016/j.aim.2013.05.016)
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Abstract
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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Li, Professor Xin |
| Authors: | Li, X. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Advances in Mathematics |
| Publisher: | Elsevier |
| ISSN: | 0001-8708 |
| ISSN (Online): | 1090-2082 |
| Published Online: | 15 June 2013 |
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