Morphisms of Cuntz-Pimsner algebras from completely positive maps

2023/11/28 by Brix, Kevin Aguyar, Mundey, Alexander, Rennie, Adam · 1 citation
#37A55 #46L08 (Secondary) #46L55 (Primary) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2311.16600

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.

Cited by

• Kernel Radon-Nikodym Derivatives for Random Matrix Products

Related

• Cuntz-Pimsner Algebras, Completely Positive Maps and Morita Equivalence
• C^*-correspondence functoriality of Cuntz-Pimsner algebras
• Essential representations of C*-correspondences
• A construction of C^*-algebras from C^*-correspondences
• Passing C^*-correspondence Relations to the Cuntz-Pimsner algebras