Triangular dissections, aperiodic tilings and Jones algebras

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dc.creatorCoquereaux, R.
dc.date1994-03-23
dc.date1995-03-27
dc.date.accessioned2026-07-07T09:01:31Z
dc.date.available2026-07-07T09:01:31Z
dc.descriptionThe Brattelli diagram associated with a given bicolored Dynkin-Coxeter graph of type $A_n$ determines planar fractal sets obtained by infinite dissections of a given triangle. All triangles appearing in the dissection process have angles that are multiples of $π/ (n+1).$ There are usually several possible infinite dissections compatible with a given $n$ but a given one makes use of $n/2$ triangle types if $n$ is even. Jones algebra with index $[ 4 \ \cos^2{π\over n+1}]^{-1}$ (values of the discrete range) act naturally on vector spaces associated with those fractal sets. Triangles of a given type are always congruent at each step of the dissection process. In the particular case $n=4$, there are isometric and the whole structure lead, after proper inflation, to aperiodic Penrose tilings. The ``tilings'' associated with other values of the index are discussed and shown to be encoded by equivalence classes of infinite sequences (with appropriate constraints) using $n/2$ digits (if $n$ is even) and generalizing the Fibonacci numbers.
dc.description14 pages. Revised version. 18 Postcript figures, a 500 kb uuencoded file called images.uu available by mosaic or gopher from gopher://cpt.univ-mrs.fr/11/preprints/94/fundamental-interactions/94-P.3020
dc.identifierhttps://arxiv.org/abs/hep-th/9403142
dc.identifierhttp://arxiv.org/abs/hep-th/9403142
dc.identifierAdv.Appl.Math. 16 (1995) 402-424
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/148347
dc.subjectHigh Energy Physics - Theory
dc.subjectFunctional Analysis
dc.subjectMetric Geometry
dc.subjectQuantum Algebra
dc.titleTriangular dissections, aperiodic tilings and Jones algebras
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