Geodesic
$C^*$-algebras associated with presentations of subshifts
Documenta mathematica, Tome 7 (2002), pp. 1-30
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A λ-graph system is a labeled Bratteli diagram with an upward shift except the top vertices. We construct a continuous graph in the sense of V. Deaconu from a λ-graph system. It yields a Renault's groupoid C∗-algebra by following Deaconu's construction. The class of these C∗-algebras generalize the class of C∗-algebras associated with subshifts and hence the class of Cuntz-Krieger algebras. They are unital, nuclear, unique C∗-algebras subject to operator relations encoded in the structure of the λ-graph systems among generating partial isometries and projections. If the λ-graph systems are irreducible (resp. aperiodic), they are simple (resp. simple and purely infinite). K-theory formulae of these C∗-algebras are presented so that we know an example of a simple and purely infinite C∗-algebra in the class of these C∗-algebras that is not stably isomorphic to any Cuntz-Krieger algebra.
DOI : 10.4171/dm/115
Classification : 37B10, 46L35
Mots-clés : groupoids, subshifts, C∗-algebras, Cuntz-Krieger algebras 
@article{10_4171_dm_115,
     author = {Kengo Matsumoto},
     title = {$C^*$-algebras associated with presentations of subshifts},
     journal = {Documenta mathematica},
     pages = {1--30},
     year = {2002},
     volume = {7},
     doi = {10.4171/dm/115},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/115/}
}
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Kengo Matsumoto. $C^*$-algebras associated with presentations of subshifts. Documenta mathematica, Tome 7 (2002), pp. 1-30. doi: 10.4171/dm/115

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