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

Authors

Nathan D. Brownlowe, University of WollongongFollow
Iain F. Raeburn, University of WollongongFollow
Sean T. Vittadello, University of WollongongFollow

RIS ID

36878

Publication Details

Brownlowe, N. D., Raeburn, I. F. & Vittadello, S. T. (2010). Exel's crossed product for non-unital C*-algebras. Mathematical Proceedings Of The Cambridge Philosophical Society, 149 (3), 423-444.

Abstract

We consider a family of dynamical systems (A, alpha, L) in which a is an endomorphism of a C*-algebra A and L is a transfer operator for a. 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.