Abstract
For each irrational number, 0<α<1, we consider the space of one dimensional almost periodic tilings obtained by the projection method using a line of slope α. On this space we put the relation generated by translation and the identification of the “singular pairs”. We represent this as a topological spaceX α with an equivalence relationR α. OnR α there is a natural locally Hausdorff topology from which we obtain a topological groupoid with a Haar system. We then construct the C*-algebra of this groupoid and show that it is the irrational rotation C*-algebra,A α.
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Communicated by A. Connes
Research supported by the Natural Sciences and Engineering Research Council of Canada and the Fields Institute for Research in Mathematical Sciences.
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Mingo, J.A. C*-Algebras associated with one dimensional almost periodic tilings. Commun.Math. Phys. 183, 307–337 (1997). https://doi.org/10.1007/BF02506409
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DOI: https://doi.org/10.1007/BF02506409