Dirac operators and spectral triples for some fractal sets built on curves

Erik Christensen; Cristina Ivan; Michel L. Lapidus

doi:10.1016/j.aim.2007.06.009

Dirac operators and spectral triples for some fractal sets built on curves

Erik Christensen, Cristina Ivan, Michel L. Lapidus

Institut for Matematiske Fag

39 Citationer (Scopus)

Abstract

Et spektralt triple er et objekt, som er beskrevet ved hjaelp af en algebra af operatorer paa et Hilbertrum, samt en ubegraenset selvadjungeret operator kaldet en Dirac operator. Denne model kan ogsaa anvendes til studiet af klassiske geometriske objekter. I artiklen konstrueres der spektrale triple associerede til fraktale delmaengder af planen, og det vises, at visse klassiske begrber som afstand, maal og Hausdorff dimension kan beregnes ud fra det spektrale triple.

Udgivelsesdato: 15 januar

Originalsprog	Engelsk
Tidsskrift	Advances in Mathematics
Vol/bind	217
Udgave nummer	1
Sider (fra-til)	42 - 78
Antal sider	37
ISSN	0001-8708
DOI	https://doi.org/10.1016/j.aim.2007.06.009
Status	Udgivet - 2008

Emneord

Det Natur- og Biovidenskabelige Fakultet
matematik
ikke kommutativ geometri

Adgang til dokumentet

10.1016/j.aim.2007.06.009

Citationsformater

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abstract = "A spectral triple is an object which is described using an algebra of operators on a Hilbert space and an unbounded self-adjoint operator, called a Dirac operator. This model may be applied to the study of classical geometrical objects .The article contains a construction of a spectral triple associated to some classical fractal subsets of the plane, and it is demonstrated that you can read of many classical geometrical structures, such as distance, measure and Hausdorff dimension from the spectral triple. ",

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KW - non commutativ geometry

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Dirac operators and spectral triples for some fractal sets built on curves

Abstract

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