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On The Algebraic Characterization of Aperiodic Tilings Related To ADE-Root Systems | | Johannes Kellendonk
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14 Oct 1992 | | Subject: | hep-th | | Abstract: | oindent 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 $K_0$-group of an algebra naturally assigned to the quantum space. The result also yields an application of the $2$-dimensional abstract gap labelling theorem. | | Source: | arXiv, hep-th/9210078 | | Services: | Forum | Review | PDF | Favorites | |
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