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

Menevşe Eryüzlü

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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.

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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.

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Available 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.

Key concepts: Morphism, Mathematics, Functor, Isomorphism (crystallography), Generalization, Pure mathematics, Morita therapy, Morita equivalence

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