Exel's Crossed Product and Relative Cuntz-Pimsner Algebras

2004/08/24 by Nathan Brownlowe, Brownlowe, Nathan, Iain Raeburn +1
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/0408324

12 pages

arxiv created 2004/08/24 · openalex publication_date 2004/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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