Year: 2001
Type: article
Abstract: 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.
Authors: Hyeong-Chai Jeong, Eunsang Kim, Chang-Yeong Lee
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2066809487