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Flow equivalence of graph algebras

  • TERESA BATES (a1) and DAVID PASK (a2)
Abstract

This paper explores the effect of various graphical constructions upon the associated graph C*-algebras. The graphical constructions in question arise naturally in the study of flow equivalence for topological Markov chains. We prove that out-splittings give rise to isomorphic graph algebras, and in-splittings give rise to strongly Morita equivalent C*-algebras. We generalize the notion of a delay as defined in (D. Drinen, Preprint, Dartmouth College, 2001) to form in-delays and out-delays. We prove that these constructions give rise to Morita equivalent graph C*-algebras. We provide examples which suggest that our results are the most general possible in the setting of the C*-algebras of arbitrary directed graphs.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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