On The Algebraic Characterization of Aperiodic Tilings Related To ADE-Root Systems
| dc.creator | Kellendonk, Johannes | |
| dc.date | 1992-10-14 | |
| dc.date | 1992-12-30 | |
| dc.date.accessioned | 2026-07-07T09:01:03Z | |
| dc.date.available | 2026-07-07T09:01:03Z | |
| dc.description | \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 $K_0$-group of an algebra naturally assigned to the quantum space. The result also yields an application of the $2$-dimensional abstract gap labelling theorem. | |
| dc.description | 29 pages LaTex, 2 figures not included (they may be send upon request), BONN-HE-92-26 | |
| dc.identifier | https://arxiv.org/abs/hep-th/9210078 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9210078 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148197 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | On The Algebraic Characterization of Aperiodic Tilings Related To ADE-Root Systems | |
| dc.type | text |