$C^*$-correspondence functoriality of Cuntz-Pimsner algebras

M. Eryüzlü

$C^*$-correspondence functoriality of Cuntz-Pimsner algebras

Operator Algebras 2020-09-29 v2

Authors: M. Eryüzlü

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.

Keywords

c*-correspondence cuntz-pimsner algebra functor morita equivalence hilbert module

Cite

@article{arxiv.2009.08488,
  title  = {$C^*$-correspondence functoriality of Cuntz-Pimsner algebras},
  author = {M. Eryüzlü},
  journal= {arXiv preprint arXiv:2009.08488},
  year   = {2020}
}

Comments

error in Theorem 5.15

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