THE GAUGE-INVARIANT UNIQUENESS THEOREMFOR RELATIVE CUNTZ-PIMSNER ALGEBRAS

We present a new proof of the gauge-invariant uniqueness theorem for C*-correspondences that is conceptual and simplifies earlier arguments. The proof is based on a reasoning due to Evgenios Kakariadis, and treats all relative Cuntz-Pimsner algebras on equal footing. As a consequence, in the spirit of Katsura's work, we obtain a classification of lattices of gauge-invariant ideals. Furthermore, we pairwise compare Cuntz-Pimsner algebras in a representation-free intrinsic manner. As an application, we extend the pullback result by Robertson and Szymański in the case of graph correspondences, and show why this extension does not apply to general C*-correspondences. Based on joint work with Piotr. M. Hajac and Mariusz Tobolski.

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