C*-algebras of tilings with infinite rotational symmetry

Details C*-algebras of tilings with infinite rotational symmetry C*-algebras of tilings with infinite rotational symmetry

2010-10-11

arxiv.org/abs/1010.1991v1

Journal of Operator Theory 64:2 (2010), p.299-319

Mathematics

Operator Algebras

Scientific paper

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.

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