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A note on the nuclear dimension of Cuntz–Pimsner
$C^*$-algebras associated with minimal shift spaces
- Part of
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- 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.
Subgroup Correspondences
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 61 / Issue 4 / November 2018
- Published online by Cambridge University Press:
- 14 August 2018, pp. 1127-1154
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