Tiling groupoids and Bratteli diagrams
type: Item
instance of: scholarly article
title: Tiling groupoids and Bratteli diagrams
zbMATH Open document ID: 1218.37024
author: Jean Bellissard
author: Antoine Julien
author: Jean Savinien
published in: Annales Henri Poincaré
publication date: 2011-02-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/0911.0080
review text: The authors describe a combinatorial way to reconstruct a tiling space and its grupoid, using Bratteli diagrams.
Mathematics Subject Classification ID: 37B50
Mathematics Subject Classification ID: 52C22
zbMATH DE Number: 5851559
zbMATH Keywords: tiling space
zbMATH Keywords: grupoid
zbMATH Keywords: Bratteli diagram
reviewed by: I. V. Andrianov
MaRDI profile type: Publication
OpenAlex ID: W2055802396
arXiv ID: 0911.0080
cites work: Affability of Euclidean tilings
cites work: Topological invariants for substitution tilings and their associated $C^\ast$-algebras
cites work: Q3752945
cites work: Hulls of aperiodic solids and gap labeling theorems
cites work: Q4823101
cites work: Spaces of tilings, finite telescopic approximations and gap-labeling
cites work: Inductive Limits of Finite Dimensional C ∗ -Algebras
cites work: Measure space automorphisms, the normalizers of their full groups, and approximate finiteness
cites work: Q4200733
cites work: Q4310044
cites work: Substitutional dynamical systems, Bratteli diagrams and dimension groups
cites work: \(K\)-groups associated with substitution minimal systems
cites work: Affable equivalence relations and orbit structure of Cantor dynamical systems
cites work: Q3424907
cites work: Orbit equivalence for Cantor minimal ℤ²-systems
cites work: The absorption theorem for affable equivalence relations
cites work: Orbit equivalence for Cantor minimal \(\mathbb Z^d\)-systems
cites work: Q3735714
cites work: ORDERED BRATTELI DIAGRAMS, DIMENSION GROUPS AND TOPOLOGICAL DYNAMICS
cites work: Tiling groupoids and Bratteli diagrams. II: Structure of the orbit equivalence relation
cites work: NONCOMMUTATIVE GEOMETRY OF TILINGS AND GAP LABELLING
cites work: The local structure of tilings and their integer group of coinvariants
cites work: Geometric models for quasicrystals. I. Delone sets of finite type
cites work: Geometric models for quasicrystals. II. Local rules under isometries
cites work: Repetitive Delone sets and quasicrystals
cites work: Affability of equivalence relations arising from two-dimensional substitution tilings
cites work: Crossed products of the Cantor set by free minimal actions of \(\mathbb Z^d\)
cites work: Substitution dynamical systems - spectral analysis
cites work: Space tilings and local isomorphism
cites work: A groupoid approach to C*-algebras
cites work: Tiling spaces are inverse limits
cites work: A spectral sequence for theK-theory of tiling spaces
cites work: Q4837266
cites work: Q4310071
cites work: Q3665726
DOI: 10.1007/S00023-010-0034-7
description: scientific article