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Exel's crossed product for non-unital C*-algebras

Published online by Cambridge University Press:  19 July 2010

NATHAN BROWNLOWE ,
IAIN RAEBURN  and
SEAN T. VITTADELLO
NATHAN BROWNLOWE
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia. e-mail: nathanb@uow.edu.au
IAIN RAEBURN
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia.
SEAN T. VITTADELLO
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia. e-mail: sean.vittadello@gmail.com
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Abstract

We consider a family of dynamical systems (A, α, L) in which α is an endomorphism of a C*-algebra A and L is a transfer operator for α. We extend Exel's construction of a crossed product to cover non-unital algebras A, and show that the C*-algebra of a locally finite graph can be realised as one of these crossed products. When A is commutative, we find criteria for the simplicity of the crossed product, and analyse the ideal structure of the crossed product.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 3 , November 2010 , pp. 423 - 444
Copyright
Copyright © Cambridge Philosophical Society 2010

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