2000/08/22 by Hyeong-Chai Jeong, Eunsang Kim, Chang-Yeong Lee · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Connection (principal bundle) #Fibonacci number #Foliation (geology) #Kronecker delta #Noncommutative geometry #Quasicrystal Structures and Properties #Space (punctuation) #Torus #cond-mat #math-ph #math.MP
paper · pdf · doi:10.1088/0305-4470/34/31/201
published in Journal of Physics A Mathematical and General 34(31), R1-R19 (Institute of Physics)
arxiv created 2000/08/22 · openalex publication_date 2001/07/27 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.