TY - JOUR

T1 - On the automorphism groups of multidimensional shifts of finite type

AU - Hochman, Michael

PY - 2010/6

Y1 - 2010/6

N2 - We investigate algebraic properties of the automorphism group of multidimensional shifts of finite type (SFTs). We show that positive entropy implies that the automorphism group contains every finite group and, together with transitivity, implies that the center of the automorphism group is trivial (i.e.consists only of the shift action). We also show that positive entropy and dense minimal points (in particular, dense periodic points) imply that the automorphism group of X contains a copy of the automorphism group of the one-dimensional full shift, and hence contains non-trivial elements of infinite order. On the other hand we construct a mixing, positive-entropy SFT whose automorphism group is, modulo the shift action, a union of finite groups.

AB - We investigate algebraic properties of the automorphism group of multidimensional shifts of finite type (SFTs). We show that positive entropy implies that the automorphism group contains every finite group and, together with transitivity, implies that the center of the automorphism group is trivial (i.e.consists only of the shift action). We also show that positive entropy and dense minimal points (in particular, dense periodic points) imply that the automorphism group of X contains a copy of the automorphism group of the one-dimensional full shift, and hence contains non-trivial elements of infinite order. On the other hand we construct a mixing, positive-entropy SFT whose automorphism group is, modulo the shift action, a union of finite groups.

UR - http://www.scopus.com/inward/record.url?scp=77955854166&partnerID=8YFLogxK

U2 - 10.1017/S0143385709000248

DO - 10.1017/S0143385709000248

M3 - Article

AN - SCOPUS:77955854166

SN - 0143-3857

VL - 30

SP - 809

EP - 840

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 3

ER -