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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.
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- Research Article
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- © 2016 Australian Mathematical Publishing Association Inc.
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