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CUNTZ–PIMSNER ALGEBRAS ASSOCIATED TO TENSOR PRODUCTS OF $C^{\ast }$-CORRESPONDENCES

Published online by Cambridge University Press:  27 October 2016

ADAM MORGAN
ADAM MORGAN*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA email anmorgan@asu.edu
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Abstract

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Given two $C^{\ast }$-correspondences $X$ and $Y$ over $C^{\ast }$-algebras $A$ and $B$, we show that (under mild hypotheses) the Cuntz–Pimsner algebra ${\mathcal{O}}_{X\otimes Y}$ embeds as a certain subalgebra of ${\mathcal{O}}_{X}\otimes {\mathcal{O}}_{Y}$ and that this subalgebra can be described in a natural way in terms of the gauge actions on ${\mathcal{O}}_{X}$ and ${\mathcal{O}}_{Y}$. We explore implications for graph algebras, crossed products by $\mathbb{Z}$, crossed products by completely positive maps, and give a new proof of a result of Kaliszewski, Quigg, and Robertson related to coactions on correspondences.

Keywords

Cuntz–Pimsnertensor productscorrespondences
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 3 , June 2017 , pp. 348 - 368
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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