Sums of two-dimensional spectral triples
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Sums of two-dimensional spectral triples. / Christensen, Erik; Ivan, Cristina.
I: Mathematica Scandinavica, Bind 100, Nr. 1, 2007, s. 35-60.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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