TY - JOUR
T1 - The Stabilized Automorphism Group of a Subshift
AU - Hartman, Yair
AU - Kra, Bryna
AU - Schmieding, Scott
N1 - Funding Information:
The authors gratefully thank Mike Boyle for helpful comments and the referees for suggesting numerous improvements. This work was supported by the Israel Science Foundation [1175/18to Y.H.]; and the National Science Foundation [1800544to B.K., 1502643to S.S.].
Publisher Copyright:
© The Author(s) 2021. Published by Oxford University Press. All rights reserved.
PY - 2022/11/1
Y1 - 2022/11/1
N2 - 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.
AB - 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.
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U2 - 10.1093/imrn/rnab204
DO - 10.1093/imrn/rnab204
M3 - Article
AN - SCOPUS:85158014246
SN - 1073-7928
VL - 2022
SP - 17112
EP - 17186
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 21
ER -