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Exel's Crossed Product and Relative Cuntz-Pimsner Algebras

Nathan Brownlowe·Iain Raeburn
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Abstract

We consider Exel's new construction of a crossed product of a C*-algebra A by an endomorphism α. 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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Nathan Brownlowe, Iain Raeburn. 2004-08-24. Exel's Crossed Product and Relative Cuntz-Pimsner Algebras. https://arxiv.org/abs/math/0408324

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