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arXiv · 2311.16600

Morphisms of Cuntz-Pimsner algebras from completely positive maps

Kevin Aguyar Brix·Alexander Mundey·Adam Rennie
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Abstract

We introduce positive correspondences as right C*-modules with left actions given by completely positive maps. Positive correspondences form a semi-category that contains the C*-correspondence (Enchilada) category as a "retract". Kasparov's KSGNS construction provides a semi-functor from this semi-category onto the C*-correspondence category. The need for left actions by completely positive maps appears naturally when we consider morphisms between Cuntz-Pimsner algebras, and we describe classes of examples arising from projections on C*-correspondences and Fock spaces, as well as examples from conjugation by bi-Hilbertian bimodules of finite index.

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Kevin Aguyar Brix, Alexander Mundey, Adam Rennie. 2023-11-28. Morphisms of Cuntz-Pimsner algebras from completely positive maps. https://arxiv.org/abs/2311.16600

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