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Preprint . 2024
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Proceedings of the American Mathematical Society
Article . 2025 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2024
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Spectral triples on noncommutative solenoids from the standard spectral triples on quantum tori

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 10 Dec 2025Embargo end date: 01 Jan 2024 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society (issn: 0002-9939, eissn: 1088-6826, Copyright policy )
Authors: Farsi, Carla; Latremoliere, Frederic; Packer, Judith;

doi: 10.1090/proc/17061 , 10.48550/arxiv.2403.16323

arXiv: 2403.16323

Spectral triples on noncommutative solenoids from the standard spectral triples on quantum tori

Abstract

We address the natural question: as noncommutative solenoids are inductive limits of quantum tori, do the standard spectral triples on quantum tori converge to some spectral triple on noncommutative solenoid for the spectral propinquity? We answer this question by showing that, using appropriate bounded perturbations of the spectral triples on quantum tori, such a spectral triple on noncommutative solenoid can be constructed.

Related Organizations
Keywords

46L89, Mathematics - Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green