TY - JOUR
T1 - Normal amenable subgroups of the automorphism group of the full shift
AU - Frisch, Joshua
AU - Schlank, Tomer
AU - Tamuz, Omer
N1 - Publisher Copyright:
© 2017 Cambridge University Press.
PY - 2019/5/1
Y1 - 2019/5/1
N2 - We show that every normal amenable subgroup of the automorphism group of the full shift is contained in its center. This follows from the analysis of this group's Furstenberg topological boundary, through the construction of a minimal and strongly proximal action. We extend this result to higher dimensional full shifts. This also provides a new proof of Ryan's theorem and of the fact that these groups contain free groups.
AB - We show that every normal amenable subgroup of the automorphism group of the full shift is contained in its center. This follows from the analysis of this group's Furstenberg topological boundary, through the construction of a minimal and strongly proximal action. We extend this result to higher dimensional full shifts. This also provides a new proof of Ryan's theorem and of the fact that these groups contain free groups.
UR - http://www.scopus.com/inward/record.url?scp=85063596732&partnerID=8YFLogxK
U2 - 10.1017/etds.2017.72
DO - 10.1017/etds.2017.72
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AN - SCOPUS:85063596732
SN - 0143-3857
VL - 39
SP - 1290
EP - 1298
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 5
ER -