Exel's Crossed Product and Relative Cuntz-Pimsner Algebras

Details Exel's Crossed Product and Relative Cuntz-Pimsner Algebras Exel's Crossed Product and Relative Cuntz-Pimsner Algebras

2004-08-24

arxiv.org/abs/math/0408324v1

Mathematics

Operator Algebras

12 pages

Scientific paper

We consider Exel's new construction of a crossed product of a C*-algebra A by an endomorphism \alpha. We prove that this crossed product is universal for an appropriate family of covariant representations, and we show that it can be realised as a relative Cuntz-Pimsner algbera. We describe a necessary and sufficient condition for the canonical map from A into the crossed product to be injective, and present several examples to demonstrate the scope of this result. We also prove a gauge-invariant uniqueness theorem for the crossed product.

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