Automorphisms of self-similar trees

2023/12/06 by Tobias Hartnick, Merlin Incerti-Medici, Hartnick, Tobias +1
Mathematics · Physics and Astronomy · #20E08 #20F65 #22D05 #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2312.03334

openalex publication_date 2023/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit of certain finite products of finite symmetric groups, which are parametrized by a certain deterministic finite automaton.

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