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MATHEMATICA SCANDINAVICA
Article . 2007 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2006
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Sums of two-dimensional spectral triples

Authors: Christensen, Erik; Ivan, Cristina;

Sums of two-dimensional spectral triples

Abstract

We study countable sums of two-dimensional modules for the continuous complex functions on a compact metric space and show that it is possible to construct a spectral triple which gives the original metric back. This spectral triple will be finitely summable for any positive parameter. We also construct a sum of two-dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in $\mathsf R$. The metric is recovered exactly, the Dixmier trace induces a multiple of the Lebesgue integral and the growth of the number of eigenvalues $N(\Lambda)$ bounded by $\Lambda$ behaves, such that $N(\Lambda)/\Lambda$ is bounded, but without limit for $\Lambda\to \infty$.

Country
Denmark
Keywords

mathematics, Mathematics - Operator Algebras, Metric Geometry (math.MG), ikke kommutativ geometri, 46L85, 58B34, Mathematics - Metric Geometry, matematik, non commutative geometry, Faculty of Science, FOS: Mathematics, /dk/atira/pure/core/keywords/TheFacultyOfScience, 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!
12
Average
Top 10%
Average
Green
bronze
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