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Non-Commutative Methods for the K-Theory of C*-Algebras of Aperiodic Patterns from Cut-and-Project Systems

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Abstract

We investigate the C*-algebras associated to aperiodic structures called model sets obtained by the cut-and-project method. These C*-algebras are Morita equivalent to crossed product C*-algebras obtained from dynamics on a disconnected version of the internal space. This construction may be made from more general data, which we call a hyperplane system. From a hyperplane system, others may be constructed by a process of reduction and we show how the C*-algebras involved are related to each other. In particular, there are natural elements in the Kasparov KK-groups for the C*-algebra of a hyperplane system and that of its reduction. The induced map on K-theory fits in a six-term exact sequence. This provides a new method of the computation of the K-theory of such C*-algebras which is done completely in the setting of non-commutative geometry.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada, V8W 3R4

    Ian F. Putnam

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  1. Ian F. Putnam
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Correspondence to Ian F. Putnam.

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Communicated by A. Connes

Supported in part by a grant from NSERC, Canada.

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Putnam, I.F. Non-Commutative Methods for the K-Theory of C*-Algebras of Aperiodic Patterns from Cut-and-Project Systems. Commun. Math. Phys. 294, 703–729 (2010). https://doi.org/10.1007/s00220-009-0968-0

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  • DOI: https://doi.org/10.1007/s00220-009-0968-0

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