Flow equivalence of graph algebras

By T. Bates, David Pask. Ergodic Theory and Dynamical Systems, 2002

77 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fe1cfd6e928affad516821296ee7af7a273c2ca8

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Citations in the corpus

Graph algebras and orbit equivalence (2014, background): “Before we state the corollary we recall the terminology of [3].”
Flow invariants in the classification of Leavitt path algebras (2008, methodology): “Proof. The proof is analogous to the proof of [ 9, Theorem 5.3 ], using the arguments of the proof of Theorem 3.3.”