Flow equivalence of graph algebras

Details Flow equivalence of graph algebras Flow equivalence of graph algebras

2002-12-18

arxiv.org/abs/math/0212241v2

Mathematics

Operator Algebras

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

Scientific paper

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 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 $C^*$-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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