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

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

2009-08-19

arxiv.org/abs/0908.2671v1

Mathematics

Operator Algebras

22 pages

Scientific paper

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 \alpha. 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.

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