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

作者：Putnam Ian F^*

来源：Communications in Mathematical Physics, 2010, 294(3): 703-729.

DOI：10.1007/s00220-009-0968-0

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.

• 出版日期2010-3