## Faculty of Engineering and Information Sciences - Papers: Part A

18844

#### Publication Details

Brownlowe, N. & Raeburn, I. (2006). Exel's crossed product and relative Cuntz-Pimsner algebras. Cambridge Philosophical Society. Mathematical Proceedings, 141 (3), 497-508.

#### Abstract

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.

COinS

#### Link to publisher version (DOI)

http://dx.doi.org/10.1017/S030500410600956X