Homomorphisms between multidimensional constant-shape substitutions

automorphism groups; digit tiles; Homomorphisms; nondeterministic directions; substitutive subshifts; Geometry and Topology; Discrete Mathematics and Combinatorics

Abstract :

[en] We study a class of Zd -substitutive subshifts, including a large family of constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms of Zd . We prove that any measurable factor map and even any homomorphism associated to a matrix commuting with the expansion matrix, induces a continuous one. We also get strong restrictions on the normalizer group, proving that any endomorphism is invertible, the normalizer group is virtually generated by the shift action and the quotient of the normalizer group by the automorphisms is restricted by the digit tile of the substitution.

Disciplines :

Mathematics

Author, co-author :

Cabezas Aros, Christopher ; Université de Liège - ULiège > Mathematics ; Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS-UMR 7352, Université de Picardie Jules Verne, Amiens, France

Language :

English

Title :

Homomorphisms between multidimensional constant-shape substitutions

Publication date :

2023

Journal title :

Groups, Geometry, and Dynamics

ISSN :

1661-7207

eISSN :

1661-7215

Publisher :

European Mathematical Society Publishing House

Volume :

Issue :

Pages :

1259 - 1323

Peer reviewed :

Peer reviewed

Data Set :

https://doi.org/10.4171/ggd/726

Available on ORBi :

since 15 January 2024

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