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A note on the nuclear dimension of Cuntz–Pimsner
$C^*$-algebras associated with minimal shift spaces
Published online by Cambridge University Press: 12 December 2022
Abstract
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.
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society
Footnotes
The authors were partially supported by a grant from the Shanghai Key Laboratory of PMMP, Science and Technology Commission of Shanghai Municipality (STCSM) (13dz2260400) and by a grant from the NNSF (11531003). The first named author was also supported by Project funded by China Postdoctoral Science Foundation under Grant2020M681221.
References
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