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Furstenberg entropy values for nonsingular actions of groups without property (T)


Author: Alexandre I. Danilenko
Journal: Proc. Amer. Math. Soc. 145 (2017), 1153-1161
MSC (2010): Primary 37A40; Secondary 37A20, 37A35
DOI: https://doi.org/10.1090/proc/13278
Published electronically: September 15, 2016
MathSciNet review: 3589315
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Abstract: Let $ G$ be a discrete countable infinite group that does not have Kazhdan's property (T) and let $ \kappa $ be a generating probability measure on $ G$. Then for each $ t>0$, there is a type $ III_1$ ergodic free nonsingular $ G$-action whose $ \kappa $-entropy (or the Furstenberg entropy) is $ t$.


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Additional Information

Alexandre I. Danilenko
Affiliation: Institute for Low Temperature Physics & Engineering of National Academy of Sciences of Ukraine, 47 Lenin Avenue, Kharkov, 61164, Ukraine
Email: alexandre.danilenko@gmail.com, alexandre.danilenko@gmail.com

DOI: https://doi.org/10.1090/proc/13278
Received by editor(s): December 16, 2015
Received by editor(s) in revised form: May 4, 2016
Published electronically: September 15, 2016
Communicated by: Nimish Shah
Article copyright: © Copyright 2016 American Mathematical Society