The Stabilized Automorphism Group of a Subshift

Author:

Hartman Yair1,Kra Bryna2,Schmieding Scott3

Affiliation:

1. Ben-Gurion University of the Negev, 8410501, Israel

2. Northwestern University, Evanston, IL 60208, USA

3. University of Denver, Denver, CO 80208, USA

Abstract

Abstract For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group, study its algebraic properties, and use them to distinguish many of the stabilized automorphism groups. We also show that for a full shift, the subgroup of the stabilized automorphism group generated by elements of finite order is simple and that the stabilized automorphism group is an extension of a free abelian group of finite rank by this simple group.

Funder

ISF

NSF

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference39 articles.

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2. Eventual extensions of finite codes;Boyle;Proc. Amer. Math. Soc.,1988

3. Nasu’s Simple Automorphisms;Boyle,1988

4. The action of inert finite-order automorphisms on finite subsystems of the shift;Boyle;Ergodic Theory Dynam. Systems,1991

5. Periodic points and automorphisms of the shift;Boyle;Trans. Amer. Math. Soc.,1987

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