Mathematische Annalen· 2026Q1
Shift equivalence relations through the lens of C*-correspondences
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- Q1SCImago
- 2026year
Short summary
Two regular C*-correspondences are strong shift equivalent if the intermediate C*-correspondences can also be chosen as regular.
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Key points
- Investigates shift equivalence relations using C*-bimodule theory.
- Shows that strong shift equivalence between regular C*-correspondences implies the existence of regular intermediate C*-correspondences.
- Provides the final result needed to answer a question by Muhly, Pask, and Tomforde.
- Confirms a conjecture by Kakariadis and Katsoulis on shift equivalence of C*-correspondences.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Mathematische Annalen, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics