Shift equivalence relations through the lens of C*-correspondences

Boris Bilich; Adam Dor-On; Efren Ruiz

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arXiv · 2411.05598

Shift equivalence relations through the lens of C*-correspondences

Boris Bilich·Adam Dor-On·Efren Ruiz

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Abstract

We continue the study of shift equivalence relations from the perspective of C*-bimodule theory. We study emerging shift equivalence relations following work of the second-named author with Carlsen and Eilers, both in terms of adjacency matrices and in terms of their C*-correspondences, and orient them when possible. In particular, we show that if two regular C*-correspondences are strong shift equivalent, then the intermediary C*-correspondences realizing the equivalence may be chosen to be regular. This result provides the final missing piece in answering a question of Muhly, Pask and Tomforde, and is used to confirm a conjecture of Kakariadis and Katsoulis on shift equivalence of C*-correspondences.

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Boris Bilich, Adam Dor-On, Efren Ruiz. 2024-11-08. Shift equivalence relations through the lens of C*-correspondences. https://arxiv.org/abs/2411.05598

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