Fractal spectral triples on Kellendonk’s C∗-algebra of a substitution tiling
نویسندگان
چکیده
منابع مشابه
Spectral triples of weighted groups
We study spectral triples on (weighted) groups and consider functors between the categories of weighted groups and spectral triples. We study the properties of weights and the corresponding functor for spectral triples coming from discrete weighted groups.
متن کاملTiling the Line with Triples
It is known the one dimensional prototile 0 a a b and its reflection 0 b a b always tile some interval. The subject has not received a great deal of further attention, although many interesting questions exist. All the information about tilings can be encoded in a finite digraph Dab We present several results about cycles and other structures in this graph. A number of conjectures and open prob...
متن کاملA Note on Spectral Triples and Quasidiagonality
The concept of a spectral triple (unbounded Fredholm module) due to A.Connes ([Co1]) is a natural noncommutative generalisation of a notion of a compact manifold, with certain summability properties corresponding in the classical case to the dimension of the manifold. Recently E.Christensen and C. Ivan established the existence of spectral triples on arbitrary AF algebras ([CI]). In this note w...
متن کاملDirac operators and spectral triples for some fractal sets built on curves
We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space. Several fractals, like a finitely summable infinite tree and the Sierpinski gasket, fit naturally within our framework. In these cases, we show that our spectral...
متن کاملA Fractal Version of the Pinwheel Tiling
Dedicated to the inspiration of Benoit Mandelbrot. The pinwheel tilings are a remarkable class of tilings of the plane, and our main goal in this paper is to introduce a fractal version of them. We will begin by describing how to construct the pinwheel tilings themselves and by discussing some of the properties that have generated so much interest. After that we will develop the fractal version...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2017
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2016.11.010