The isomorphism problem for semigroup C*-algebras of right-angled Artin monoids

Eilers, S., Li, X. and Ruiz, E. (2016) The isomorphism problem for semigroup C*-algebras of right-angled Artin monoids. Documenta Mathematica, 21, pp. 309-343.

Abstract

Semigroup C*-algebras for right-angled Artin monoids were introduced and studied by Crisp and Laca. In the paper at hand, we are able to present the complete answer to their question of when such C*-algebras are isomorphic. The answer to this question is presented both in terms of properties of the graph defining the Artin monoids as well as in terms of classification by K-theory, and is obtained using recent results from classification of non-simple C*-algebras. Moreover, we are able to answer another natural question: Which of these semigroup C*-algebras for right-angled Artin monoids are isomorphic to graph algebras? We give a complete answer, and note the consequence that many of the C*-algebras under study are semiprojective.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Li, Professor Xin
• Authors: Eilers, S., Li, X., and Ruiz, E.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Documenta Mathematica
• Publisher: Deutsche Mathematiker Vereinigung
• ISSN: 1431-0635
• ISSN (Online): 1431-0643
• Copyright Holders: Copyright © 2016 The Authors
• First Published: First published in Documenta Mathematica 21: 309-343
• Publisher Policy: Reproduced in accordance with the publisher copyright policy