C^*-correspondence functoriality of Cuntz-Pimsner algebras

2020/09/17 by Eryüzlü, M.
#2020 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2009.08488

Abstract

We construct a functor that maps C^*-correspondences to their Cuntz-Pimsner algebras. The objects in our domain category are C^*-correspondences, and the morphisms are the isomorphism classes of C^*-correspondences satisfying certain conditions. As an application, we recover a well-known result of Muhly and Solel. In fact, we show that functoriality leads us to a more generalized result: strongly Morita equivalent C^*-correspondences have Morita equivalent Cuntz-Pimsner algebras.

Related

• Passing C^*-correspondence Relations to the Cuntz-Pimsner algebras
• Functoriality of Cuntz-Pimsner correspondence maps
• Exactness of the Cuntz-Pimsner Construction
• Cuntz-Pimsner Algebras, Completely Positive Maps and Morita Equivalence
• A construction of C^*-algebras from C^*-correspondences