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A note on the nuclear dimension of Cuntz–Pimsner $C^*$-algebras associated with minimal shift spaces
Part of
- Ergodic theory
- Selfadjoint operator algebras
Zhuofeng He, Sihan Wei
Journal:

Canadian Journal of Mathematics / Volume 76 / Issue 1 / February 2024

Published online by Cambridge University Press:

12 December 2022, pp. 104-125

Print publication:

February 2024
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For every minimal one-sided shift space X over a finite alphabet, left special elements are those points in X having at least two preimages under the shift operation. In this paper, we show that the Cuntz–Pimsner $C^*$-algebra $\mathcal {O}_X$ has nuclear dimension $1$ when X is minimal and the number of left special elements in X is finite. This is done by describing concretely the cover of X, which also recovers an exact sequence, discovered before by Carlsen and Eilers.