Flow equivalence of graph algebras

Authors

David A. Pask, University of WollongongFollow
Teresa G. Bates, University of New South Wales

RIS ID

17455

Publication Details

Bates, T. G. & Pask, D. A. (2004). Flow equivalence of graph algebras. Ergodic Theory and Dynamical Systems, 24 (2), 367-382. Copyright Cambridge University Press 2004.

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.