Description

In this paper we describe a new method of defining C*-algebras from oriented combinatorial data, thereby generalizing the construction of algebras from directed graphs, higher-rank graphs, and ordered groups. We show that only the most elementary notions of concatenation and

In this paper we describe a new method of defining C*-algebras from oriented combinatorial data, thereby generalizing the construction of algebras from directed graphs, higher-rank graphs, and ordered groups. We show that only the most elementary notions of concatenation and cancellation of paths are required to define versions of Cuntz-Krieger and Toeplitz-Cuntz-Krieger algebras, and the presentation by generators and relations follows naturally. We give sufficient conditions for the existence of an AF core, hence of the nuclearity of the C*-algebras, and for aperiodicity, which is used to prove the standard uniqueness theorems.

Downloads
PDF (504.4 KB)

Details

Title
  • Groupoids and C*-Algebras for Categories of Paths
Contributors
Date Created
2014-11-01
Resource Type
  • Text
  • Collections this item is in
    Identifier
    • Digital object identifier: 10.1090/S0002-9947-2014-06008-X
    • Identifier Type
      International standard serial number
      Identifier Value
      1088-6850
    • Identifier Type
      International standard serial number
      Identifier Value
      0002-9947
    Note
    • This is the author's final accepted manuscript. The final version was first published in TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY in 366 (2014), published by the American Mathematical Society at http://dx.doi.org/10.1090/S0002-9947-2014-06008-X

    Citation and reuse

    Cite this item

    This is a suggested citation. Consult the appropriate style guide for specific citation guidelines.

    Spielberg, Jack (2014). GROUPOIDS AND C*-ALGEBRAS FOR CATEGORIES OF PATHS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 366(11), 5771-5819. http://dx.doi.org/10.1090/S0002-9947-2014-06008-X

    Machine-readable links