Flow equivalence of graph algebras

Abstract

This paper explores the effect of various graphical constructions upon the associated graph $C^{\ast }$-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 $C^{\ast }$-algebras. We generalise the notion of a delay as defined by Drinen to form in-delays and out-delays. We prove that these constructions give rise to Morita equivalent graph $C^{\ast }$-algebras. We provide examples which suggest that our results are the most general possible in the setting of the $C^{\ast }$-algebras of arbitrary directed graphs.

14 pages with various embedded pictures. Updated version now to appear in Ergodic Theory and Dynamical systems

References in corpus (2)

• Skew products and crossed products by coactions
• C*-equivalences of graphs