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

Abstract

We consider a family of dynamical systems (A,alpha,L) in which alpha 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.

arXiv comment22 pages

Cited by in corpus (5)

• Crossed products by endomorphisms and reduction of relations in relative Cuntz-Pimsner algebras
• Topological aperiodicity for product systems over semigroups of Ore type
• Crossed products for interactions and graph algebras
• Ideal structure of crossed products by endomorphisms via reversible extensions of $C^{\ast }$-dynamical systems
• Topological freeness for $C^{\ast }$-correspondences