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

Menevşe Eryüzlü

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

Operator Algebras 2024-10-02 v3

Authors: Menevşe Eryüzlü

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.

Keywords

c*-correspondences cuntz-pimsner algebras functor morita equivalence strong shift equivalence

Cite

@article{arxiv.2107.10486,
  title  = {Passing $C^*$-correspondence Relations to the Cuntz-Pimsner algebras},
  author = {Menevşe Eryüzlü},
  journal= {arXiv preprint arXiv:2107.10486},
  year   = {2024}
}

Comments

This paper is a replacement for arXiv:2009.08488v2 (more information can be found in the introduction section). The only change in this new version is a correction of the arXiv number in the Comments

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

Abstract

Keywords

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