Distortion and the automorphism group of a shift
| Autor: | Bryna Kra, John Franks, Van Cyr, Samuel Petite |
|---|---|
| Přispěvatelé: | Bucknell University Departement of Mathematics, Umicore Coating Services, Department of Mathematics, Northwestern University, Northwestern University, Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 (LAMFA), Université de Picardie Jules Verne (UPJV)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2018 |
| Předmět: |
Automorphism group
Algebra and Number Theory Computer Science::Information Retrieval Applied Mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 010102 general mathematics Dynamical Systems (math.DS) Automorphism 01 natural sciences Combinatorics Low complexity Mathematics::Group Theory Nilpotent 0103 physical sciences FOS: Mathematics Embedding Countable set 010307 mathematical physics Mathematics - Dynamical Systems 0101 mathematics ComputingMilieux_MISCELLANEOUS Analysis Mathematics |
| Zdroj: | Journal of modern dynamics Journal of modern dynamics, American Institute of Mathematical Sciences, 2018, 13 (1), pp.147-161. ⟨10.3934/jmd.2018015⟩ |
| ISSN: | 1930-532X 1930-5311 |
| DOI: | 10.3934/jmd.2018015 |
| Popis: | The set of automorphisms of a one-dimensional subshift \begin{document} $(X, σ)$ \end{document} forms a countable, but often very complicated, group. For zero entropy shifts, it has recently been shown that the automorphism group is more tame. We provide the first examples of countable groups that cannot embed into the automorphism group of any zero entropy subshift. In particular, we show that the Baumslag-Solitar groups \begin{document} ${\rm BS}(1,n)$ \end{document} and all other groups that contain exponentially distorted elements cannot embed into \begin{document} ${\rm Aut}(X)$ \end{document} when \begin{document} $h_{{\rm top}}(X) = 0$ \end{document} . We further show that distortion in nilpotent groups gives a nontrivial obstruction to embedding such a group in any low complexity shift. |
| Databáze: | OpenAIRE |
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