Eilers, Søren; Li, Xin; Ruiz, Efren

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

Doc. Math., J. DMV 21, 309-343 (2016)


Summary: 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.

Mathematics Subject Classification

46L05, 20F36, 20M05, 46L35