A class of limit algebras associated with directed graphs

• Autores: David W. Kribs, Baruch Solel
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 82, Nº 3, 2007, págs. 345-368
• Idioma: inglés
• DOI: 10.1017/s1446788700036168
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• Resumen

  • Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C*-algebras. We prove the algebras generated by all shifts of a fixed period are of Cuntz-Krieger and Toeplitz-Cuntz-Krieger type. The limit C*-algebras determined by an increasing sequence of positive integers, each dividing the next, are proved to be isomorphic to Cuntz-Pimsner algebras and the linking maps are shown to arise as factor maps. We derive a characterization of simplicity and compute the K-groups for these algebras. We prove a classification theorem for the class of algebras generated by simple loop graphs.