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

Abstract

We consider a family of dynamical systems (A, α, L) in which 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. © Cambridge Philosophical Society 2010.