C*-algebras of tilings with infinite rotational symmetry
Operator Algebras
2010-10-12 v1
Abstract
A tiling with infinite rotational symmetry, such as the Conway-Radin Pinwheel Tiling, gives rise to a topological dynamical system to which an \'etale equivalence relation is associated. A groupoid C*-algebra for a tiling is produced and a separating dense set is exhibited in the C*-algebra which encodes the structure of the topological dynamical system. In the case of a substitution tiling, natural subsets of this separating dense set are used to define an AT-subalgebra of the C*-algebra. Finally our results are applied to the Pinwheel Tiling.
Keywords
Cite
@article{arxiv.1010.1991,
title = {C*-algebras of tilings with infinite rotational symmetry},
author = {Michael F. Whittaker},
journal= {arXiv preprint arXiv:1010.1991},
year = {2010}
}