Fibonacci链经叶化的非对易环面
Noncommutative Torus from Fibonacci Chains via Foliation
摘要：
本文利用Fibonacci链的指数序列对Fibonacci链进行了分类，并在F链空间上构造了一个近似有限维（AF）的$C^*$ -代数.关于这个AF-代数的K-理论表明了非交换环面和F-链空间之间的联系。一个非交换环面可以看作是环面上叶状的$C^*$ -代数，它被显式嵌入到F-链空间上的AF-代数中。作为其对应，我们利用构造F-链的割过程得到了F-链空间与环面上Kronecker叶状的叶空间之间的关系。
英文摘要：
We classify the Fibonacci chains (F-chains) by their index sequences and construct an approximately finite dimensional (AF) $C^*$-algebra on the space of F-chains as Connes did on the space of Penrose tiling. The K-theory on this AF-algebra suggests a connection between the noncommutative torus and the space of F-chains. A noncommutative torus, which can be regarded as the $C^*$-algebra of a foliation on the torus, is explicitly embedded into the AF-algebra on the space of F-chains. As a counterpart of that, we obtain a relation between the space of F-chains and the leaf space of Kronecker foliation on the torus using the cut-procedure of constructing F-chains.
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