The isomorphism problem for semigroup -algebras of right-angled Artin monoids
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.
Cite this article
Søren Eilers, Xin Li, Efren Ruiz, The isomorphism problem for semigroup -algebras of right-angled Artin monoids. Doc. Math. 21 (2016), pp. 309–343DOI 10.4171/DM/535