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arXiv · 1409.6632

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

Søren Eilers·Xin Li·Efren Ruiz
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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.

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Søren Eilers, Xin Li, Efren Ruiz. 2014-09-23. The isomorphism problem for semigroup C*-algebras of right-angled Artin monoids. https://arxiv.org/abs/1409.6632

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