Noncommutative Torus from Fibonacci Chains via Foliation
Mathematical Physics
2009-10-31 v1 Condensed Matter
math.MP
Abstract
We classify the Fibonacci chains (F-chains) by their index sequences and construct an approximately finite dimensional (AF) -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 -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.
Cite
@article{arxiv.math-ph/0008028,
title = {Noncommutative Torus from Fibonacci Chains via Foliation},
author = {Hyeong-Chai Jeong and Eunsang Kim and Chang-Yeong Lee},
journal= {arXiv preprint arXiv:math-ph/0008028},
year = {2009}
}