Journal of Operator Theory

Volume 78, Issue 2, Fall 2017 pp. 309-345.

On Exel-Pardo algebras

Authors: Erik Bedos (1), S. Kaliszewski (2), and John Quigg (3)
Author institution:(1) Institute of Mathematics, University of Oslo, PB 1053 Blindern, 0316 Oslo, Norway
(2) School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, U.S.A.
(3) School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, U.S.A.

Summary: We generalize a recent construction of Exel and Pardo, from discrete groups acting on finite directed graphs to locally compact groups acting on topological graphs. To each cocycle for such an action, we construct a $C^*$-correspondence whose associated Cuntz-Pimsner algebra is the analog of the Exel--Pardo $C^*$-algebra.

DOI: http://dx.doi.org/10.7900/jot.2016aug16.2118
Keywords: groups, graphs, cocycles, self-similarity, $C^*$-correspondences, Toeplitz algebras, Cuntz-Pimsner algebras

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