1992/10/14 by Johannes Kellendonk, Kellendonk, Johannes
Computer Science · Materials Science · #Cellular Automata and Applications #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quasicrystal Structures and Properties #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.hep-th/9210078
openalex publication_date 1992/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
\noindent The algebraic characterization of classes of locally isomorphic aperiodic tilings, being examples of quantum spaces, is conducted for a certain type of tilings in a manner proposed by A. Connes. These 2-dimensional tilings are obtained by application of the strip method to the root lattice of an ADE-Coxeter group. The plane along which the strip is constructed is determined by the canonical Coxeter element leading to the result that a 2-dimensional tiling decomposes into a cartesian product of two 1-dimensional tilings. The properties of the tilings are investigated, including selfsimilarity, and the determination of the relevant algebraic invariant is considered, namely the ordered K0-group of an algebra naturally assigned to the quantum space. The result also yields an application of the 2-dimensional abstract gap labelling theorem.