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Higher rank graph C*-algebras

Journal Article


Abstract

  • Building on recent work of Robertson and Steger, we associate a C*-algebra to a combinatorial object which may be thought of as a higher rank graph. This C*-algebra is shown to be isomorphic to that of the associated path groupoid. Various results in this paper give sufficient conditions on the higher rank graph for the associated C*-algebra to be: simple, purely infinite and AF. Results concerning the structure of crossed products by certain natural actions of discrete groups are obtained; a technique for constructing rank 2 graphs from "commuting" rank 1 graphs is given.

Publication Date

  • 2000

Citation

  • Kumjian, A., & Pask, D. (2000). Higher rank graph C*-algebras. New York Journal of Mathematics, 6, 1-20.

Scopus Eid

  • 2-s2.0-0001872445

Web Of Science Accession Number

Start Page

  • 1

End Page

  • 20

Volume

  • 6

Abstract

  • Building on recent work of Robertson and Steger, we associate a C*-algebra to a combinatorial object which may be thought of as a higher rank graph. This C*-algebra is shown to be isomorphic to that of the associated path groupoid. Various results in this paper give sufficient conditions on the higher rank graph for the associated C*-algebra to be: simple, purely infinite and AF. Results concerning the structure of crossed products by certain natural actions of discrete groups are obtained; a technique for constructing rank 2 graphs from "commuting" rank 1 graphs is given.

Publication Date

  • 2000

Citation

  • Kumjian, A., & Pask, D. (2000). Higher rank graph C*-algebras. New York Journal of Mathematics, 6, 1-20.

Scopus Eid

  • 2-s2.0-0001872445

Web Of Science Accession Number

Start Page

  • 1

End Page

  • 20

Volume

  • 6