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Flow equivalence of graph algebras

Published online by Cambridge University Press:  09 March 2004

TERESA BATES  and
DAVID PASK
TERESA BATES
Affiliation:
University of New South Wales, Sydney NSW 2052, Australia (e-mail: teresa@maths.unsw.edu.au)
DAVID PASK
Affiliation:
The University of Newcastle, Callaghan, NSW 2308, Australia (e-mail: davidp@maths.newcastle.edu.au)
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 2 , April 2004 , pp. 367 - 382
Copyright
2004 Cambridge University Press

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