A Groupoid C*-algebra of Observables for Quasicrystal Tilings
by
Alan L. T. Paterson
University of Mississippi

Quasicrystals are studied through their quasilattices. These are tilings of Euclidean spaces and include the Penrose tilings. J. Kellendonk has studied, using K-theoretic techniques, the gap labelling of the spectrum of Schrödinger operators on such tilings. For this purpose, he constructed a C^*-algebra of observables on the tiling. This algebra is the C^*-algebra of a certain r-discrete groupoid. The talk describes an alternative approach to the construction of such a groupoid using a groupoid associated with the directed path of pointed pattern classes for the tiling.

Date received: March 6, 1999