Journal of Operator Theory

Volume 57, Issue 2, Spring 2007 pp. 391-407.

New $C^*$-algebras from substitution tilings

Authors: Daniel Goncalves
Author institution: Departamento de Matematica, Universidade Federal de Santa Catarina, Florian Olis, 88.040-900, Brasil

Summary: Given a tiling with finite local complexity and a finite number of patterns up to translation , we associate a $C^*$-algebra to it. We show that this $C^*$-algebra is a recursive subhomogeneous algebra and characterize its ideals. In the case of a substitution tiling, that also has primitivity and recognizability, we use the construction mentioned above, on each of the inflated tilings, to obtain an inductive limit $C^*$-algebra that encodes the dynamics of the inflation map. We show that this $C^*$-algebra is simple.

Keywords: $C^*$-algebras, tilings, substitution tilings, operator algebras

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