Sums of two-dimensional spectral triples

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Sums of two-dimensional spectral triples. / Christensen, Erik; Ivan, Cristina.

In: Mathematica Scandinavica, Vol. 100, No. 1, 2007, p. 35-60.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Christensen, E & Ivan, C 2007, 'Sums of two-dimensional spectral triples', Mathematica Scandinavica, vol. 100, no. 1, pp. 35-60.

APA

Christensen, E., & Ivan, C. (2007). Sums of two-dimensional spectral triples. Mathematica Scandinavica, 100(1), 35-60.

Vancouver

Christensen E, Ivan C. Sums of two-dimensional spectral triples. Mathematica Scandinavica. 2007;100(1):35-60.

Author

Christensen, Erik ; Ivan, Cristina. / Sums of two-dimensional spectral triples. In: Mathematica Scandinavica. 2007 ; Vol. 100, No. 1. pp. 35-60.

Bibtex

@article{0c969ec09f2b11dcbee902004c4f4f50,
title = "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. The metric is recovered exactly, the Dixmier trace induces a multiple of the Lebesgue integral but the growth of the number of eigenvalues is different from the one found for the standard differential operator on the unit interval.",
keywords = "Faculty of Science, matematik, ikke kommutativ geometri, mathematics, non commutative geometry",
author = "Erik Christensen and Cristina Ivan",
year = "2007",
language = "English",
volume = "100",
pages = "35--60",
journal = "Mathematica Scandinavica",
issn = "0025-5521",
publisher = "Aarhus Universitet * Mathematica Scandinavica",
number = "1",

}

RIS

TY - JOUR

T1 - Sums of two-dimensional spectral triples

AU - Christensen, Erik

AU - Ivan, Cristina

PY - 2007

Y1 - 2007

N2 - 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. The metric is recovered exactly, the Dixmier trace induces a multiple of the Lebesgue integral but the growth of the number of eigenvalues is different from the one found for the standard differential operator on the unit interval.

AB - 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. The metric is recovered exactly, the Dixmier trace induces a multiple of the Lebesgue integral but the growth of the number of eigenvalues is different from the one found for the standard differential operator on the unit interval.

KW - Faculty of Science

KW - matematik

KW - ikke kommutativ geometri

KW - mathematics

KW - non commutative geometry

M3 - Journal article

VL - 100

SP - 35

EP - 60

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

SN - 0025-5521

IS - 1

ER -

ID: 1631927