Noncommutative torus from Fibonacci chains via foliation
Noncommutative torus from Fibonacci chains via foliation
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通过叶状结构从斐波那契链得出非交换环面
DOI：
10.1088/0305-4470/34/31/201
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
Chang
中科院分区：
文献类型：
--
作者：
Hyeong;Eunsang Kim;Chang
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）C ~*-代数。这个AF代数上的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，可以看作是环面上的叶状的C*-代数，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。我们对叶状的C*-代数的嵌入与Landi，Lizzi，和Szabo最近的结果一致，即非交换环面的C*-代数可以嵌入到AF代数中.
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. Our embedding of the C*-algebra of the foliation is consistent with the recent result of Landi, Lizzi, and Szabo that the C*-algebra of noncommutative torus can be embedded into an AF algebra.