Geodesic
The isomorphism problem for semigroup $C^*$-algebras of right-angled Artin monoids
Documenta mathematica, Tome 21 (2016), pp. 309-343
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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.
DOI : 10.4171/dm/535
Classification : 20F36, 20M05, 46L05, 46L35 
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     author = {S{\o}ren Eilers and Xin Li and Efren Ruiz},
     title = {The isomorphism problem for semigroup $C^*$-algebras of right-angled {Artin} monoids},
     journal = {Documenta mathematica},
     pages = {309--343},
     year = {2016},
     volume = {21},
     doi = {10.4171/dm/535},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/535/}
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Søren Eilers; Xin Li; Efren Ruiz. The isomorphism problem for semigroup $C^*$-algebras of right-angled Artin monoids. Documenta mathematica, Tome 21 (2016), pp. 309-343. doi: 10.4171/dm/535

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