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Group actions on topological graphs

Published online by Cambridge University Press:  16 September 2011

VALENTIN DEACONU ,
ALEX KUMJIAN  and
JOHN QUIGG
VALENTIN DEACONU
Affiliation:
Department of Mathematics, University of Nevada, Reno, NV 89557-0084, USA (email: vdeaconu@unr.edu, alex@unr.edu)
ALEX KUMJIAN
Affiliation:
Department of Mathematics, University of Nevada, Reno, NV 89557-0084, USA (email: vdeaconu@unr.edu, alex@unr.edu)
JOHN QUIGG
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, USA (email: quigg@asu.edu)
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Abstract

We define the action of a locally compact group G on a topological graph E. This action induces a natural action of G on the C*-correspondence ℋ(E) and on the graph C*-algebra C*(E). If the action is free and proper, we prove that C*(E)⋊rG is strongly Morita equivalent to C*(E/G) . We define the skew product of a locally compact group G by a topological graph E via a cocycle c:E1 →G. The group acts freely and properly on this new topological graph E×cG. If G is abelian, there is a dual action on C* (E) such that . We also define the fundamental group and the universal covering of a topological graph.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 5: Daniel J. Rudolph – in Memoriam , October 2012 , pp. 1527 - 1566
Copyright
Copyright © Cambridge University Press 2011

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