Passing C^*-correspondence Relations to the Cuntz-Pimsner algebras

2021/07/22 by Eryüzlü, Menevşe
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2107.10486

Abstract

We construct a functor that maps C^*-correspondences to their Cuntz-Pimsner algebras. Applications include a generalization of the well-known result of Muhly and Solel: Morita equivalent C^*-correspondences have Morita equivalent Cuntz-Pimsner algebras; as well as the result of Muhly, Pask, and Tomforde: regular strong shift equivalent C^*-correspondences have Morita equivalent Cuntz-Pimsner algebras.

Related

• C^*-correspondence functoriality of Cuntz-Pimsner algebras
• Strong Shift Equivalence of C^*-correspondences
• Functoriality of Cuntz-Pimsner correspondence maps
• A construction of C^*-algebras from C^*-correspondences
• Cuntz-Pimsner Algebras, Completely Positive Maps and Morita Equivalence