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arXiv · 1510.04959

Cuntz-Pimsner Algebras Associated to Tensor Products of Correspondences

Adam Morgan
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Abstract

Given two correspondences X and Y, we show that (under mild hypotheses) the Cuntz-Pimsner algebra of the tensor product of X and Y embeds as a certain subalgebra of the tensor product of the Cuntz-Pimsner algebra of X and the Cuntz=Pimsner algebra of Y. Furthermore, this subalgebra can be described in a natural way in terms of the gauge actions on the Cuntz-Pimsner algebras. We explore implications for graph algebras, crossed products by the integers, and crossed products by completely positive maps. We also give a new proof of a result of Kaliszewski and Quigg related to coactions on correspondences.

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Adam Morgan. 2015-10-16. Cuntz-Pimsner Algebras Associated to Tensor Products of Correspondences. https://arxiv.org/abs/1510.04959

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