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C∗-algebras of labelled graphs III—K-theory computations

Journal Article


Abstract


  • In this paper we give a formula for the (Formula presented.)-theory of the (Formula presented.)-algebra of a weakly left-resolving labelled space. This is done by realizing the (Formula presented.)-algebra of a weakly left-resolving labelled space as the Cuntz–Pimsner algebra of a (Formula presented.)-correspondence. As a corollary, we obtain a gauge-invariant uniqueness theorem for the (Formula presented.)-algebra of any weakly left-resolving labelled space. In order to achieve this, we must modify the definition of the (Formula presented.)-algebra of a weakly left-resolving labelled space. We also establish strong connections between the various classes of (Formula presented.)-algebras that are associated with shift spaces and labelled graph algebras. Hence, by computing the (Formula presented.)-theory of a labelled graph algebra, we are providing a common framework for computing the (Formula presented.)-theory of graph algebras, ultragraph algebras, Exel–Laca algebras, Matsumoto algebras and the (Formula presented.)-algebras of Carlsen. We provide an inductive limit approach for computing the (Formula presented.)-groups of an important class of labelled graph algebras, and give examples.

Authors


  •   Bates, Teresa G. (external author)
  •   Carlsen, Toke Meier. (external author)
  •   Pask, David A.

Publication Date


  • 2017

Citation


  • Bates, T., Carlsen, T. Meier. & Pask, D. (2017). C∗-algebras of labelled graphs III—K-theory computations. Ergodic Theory and Dynamical Systems, 37 (2), 337-368.

Scopus Eid


  • 2-s2.0-84943791999

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5299

Has Global Citation Frequency


Number Of Pages


  • 31

Start Page


  • 337

End Page


  • 368

Volume


  • 37

Issue


  • 2

Place Of Publication


  • United Kingdom

Abstract


  • In this paper we give a formula for the (Formula presented.)-theory of the (Formula presented.)-algebra of a weakly left-resolving labelled space. This is done by realizing the (Formula presented.)-algebra of a weakly left-resolving labelled space as the Cuntz–Pimsner algebra of a (Formula presented.)-correspondence. As a corollary, we obtain a gauge-invariant uniqueness theorem for the (Formula presented.)-algebra of any weakly left-resolving labelled space. In order to achieve this, we must modify the definition of the (Formula presented.)-algebra of a weakly left-resolving labelled space. We also establish strong connections between the various classes of (Formula presented.)-algebras that are associated with shift spaces and labelled graph algebras. Hence, by computing the (Formula presented.)-theory of a labelled graph algebra, we are providing a common framework for computing the (Formula presented.)-theory of graph algebras, ultragraph algebras, Exel–Laca algebras, Matsumoto algebras and the (Formula presented.)-algebras of Carlsen. We provide an inductive limit approach for computing the (Formula presented.)-groups of an important class of labelled graph algebras, and give examples.

Authors


  •   Bates, Teresa G. (external author)
  •   Carlsen, Toke Meier. (external author)
  •   Pask, David A.

Publication Date


  • 2017

Citation


  • Bates, T., Carlsen, T. Meier. & Pask, D. (2017). C∗-algebras of labelled graphs III—K-theory computations. Ergodic Theory and Dynamical Systems, 37 (2), 337-368.

Scopus Eid


  • 2-s2.0-84943791999

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5299

Has Global Citation Frequency


Number Of Pages


  • 31

Start Page


  • 337

End Page


  • 368

Volume


  • 37

Issue


  • 2

Place Of Publication


  • United Kingdom