Fractals in Noncommutative Geometry

Details Fractals in Noncommutative Geometry Fractals in Noncommutative Geometry

2001-02-27

arxiv.org/abs/math/0102209v1

in the Proceedings of the Conference "Mathematical Physics in Mathematics and Physics", Siena 2000, R. Longo Ed., Fields Insti

Mathematics

Operator Algebras

15 pages, LaTeX with fic-l.cls at ftp://ftp.ams.org/pub/author-info/packages/fic/amslatex/fic-l.cls To appear in the proceed

Scientific paper

To any spectral triple (A,D,H) a dimension d is associated, in analogy with the Hausdorff dimension for metric spaces. Indeed d is the unique number, if any, such that |D|^-d has non trivial logarithmic Dixmier trace. Moreover, when d is finite non-zero, there always exists a singular trace which is finite nonzero on |D|^-d, giving rise to a noncommutative integration on A. Such results are applied to fractals in R, using Connes' spectral triple, and to limit fractals in R^n, a class which generalises self-similar fractals, using a new spectral triple. The noncommutative dimension or measure can be computed in some cases. They are shown to coincide with the (classical) Hausdorff dimension and measure in the case of self-similar fractals.

Affiliated with

Also associated with

No associations

Rating

Fractals in Noncommutative Geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fractals in Noncommutative Geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fractals in Noncommutative Geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-563455