On extensions of subshifts by finite groups

DOI10.1080/14689367.2016.1278430zbMATH Open1379.37040arXiv1509.03307OpenAlexW2963195310MaRDI QIDQ4599278

Kengo Matsumoto

Publication date: 22 December 2017

Published in: Dynamical Systems (Search for Journal in Brave)

Abstract: $lambda$-graph systems are labeled Bratteli diagram with shift operations. They present subshifts. Their matrix presentations are called symbolic matrix systems. We define skew products of $lambda$-graph systems and study extensions of subshifts by finite groups. We prove that two canonical symbolic matrix systems are $G$-strong shift equivalent if and only if their presented subshifts are $G$-conjugate. $G$-equivalent classes of subshifts are classified by the cohomology classes of their associated skewing functions.

Full work available at URL: https://arxiv.org/abs/1509.03307

zbMATH Keywords

topological conjugacyfinite groupsubshiftskewing functionstrong shift equivalence\(\lambda\)-graph system

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Symbolic dynamics (37B10) Dynamical systems and the theory of (C^*)-algebras (37A55)

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