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CUNTZ–PIMSNER ALGEBRAS ASSOCIATED TO TENSOR PRODUCTS OF
$C^{\ast }$-CORRESPONDENCES
Published online by Cambridge University Press: 27 October 2016
Abstract
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.
- Type
- Research Article
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- Copyright
- © 2016 Australian Mathematical Publishing Association Inc.
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