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C*-algebras of directed graphs and group actions

Journal Article


Abstract


  • Given a free action of a group G on a directed graph E we show that the crossed product of C*(E), the universal C*-algebra of E, by the induced action is strongly Morita equivalent to C*(E/G). Since every connected graph E may be expressed as the quotient of a tree T by an action of a free group G we may use our results to show that C*(E) is strongly Monta equivalent to the crossed product C0(∂T) × G, where ∂T is a certain zero-dimensional space canonically associated to the tree.

Publication Date


  • 1999

Citation


  • Kumjian, A., & Pask, D. (1999). C*-algebras of directed graphs and group actions. Ergodic Theory and Dynamical Systems, 19(6), 1503-1519. doi:10.1017/S0143385799151940

Scopus Eid


  • 2-s2.0-0040205692

Start Page


  • 1503

End Page


  • 1519

Volume


  • 19

Issue


  • 6

Abstract


  • Given a free action of a group G on a directed graph E we show that the crossed product of C*(E), the universal C*-algebra of E, by the induced action is strongly Morita equivalent to C*(E/G). Since every connected graph E may be expressed as the quotient of a tree T by an action of a free group G we may use our results to show that C*(E) is strongly Monta equivalent to the crossed product C0(∂T) × G, where ∂T is a certain zero-dimensional space canonically associated to the tree.

Publication Date


  • 1999

Citation


  • Kumjian, A., & Pask, D. (1999). C*-algebras of directed graphs and group actions. Ergodic Theory and Dynamical Systems, 19(6), 1503-1519. doi:10.1017/S0143385799151940

Scopus Eid


  • 2-s2.0-0040205692

Start Page


  • 1503

End Page


  • 1519

Volume


  • 19

Issue


  • 6