Ergodic Theory and Dynamical Systems



Flow equivalence of graph algebras


TERESA BATES a1 and DAVID PASK a2
a1 University of New South Wales, Sydney NSW 2052, Australia (e-mail: [email protected])
a2 The University of Newcastle, Callaghan, NSW 2308, Australia (e-mail: [email protected])

Article author query
bates t   [Google Scholar] 
pask d   [Google Scholar] 
 

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.

(Received January 7 2003)
(Revised November 2 2003)