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Normal amenable subgroups of the automorphism group of the full shift

Published online by Cambridge University Press:  07 September 2017

JOSHUA FRISCH ,
TOMER SCHLANK  and
OMER TAMUZ
JOSHUA FRISCH
Affiliation:
California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA email [email protected], [email protected]
TOMER SCHLANK
Affiliation:
Hebrew University, Givat Ram, Jerusalem, Israel email [email protected]
OMER TAMUZ
Affiliation:
California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA email [email protected], [email protected]
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Abstract

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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 5 , May 2019 , pp. 1290 - 1298
Copyright
© Cambridge University Press, 2017 

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