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Harmonic models and Bernoullicity

Part of: Ergodic theory Locally compact groups and their algebras

Published online by Cambridge University Press:  19 August 2021

Ben Hayes
Ben Hayes*
Affiliation:
Department of Mathematics, University of Virginia, 141 Cabell Drive, Kerchof Hall, Charlottesville, VA 22904, USA brh5c@virginia.edu
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Abstract

We give many examples of algebraic actions which are factors of Bernoulli shifts. These include certain harmonic models over left-orderable groups of large enough growth, as well as algebraic actions associated to certain lopsided elements in any left-orderable group. For many of our examples, the acting group is amenable so these actions are Bernoulli (and not just a factor of a Bernoulli), but there is no obvious Bernoulli partition.

Keywords

Harmonic modelalgebraic actionsBernoulli shift

MSC classification

Primary: 37A15: General groups of measure-preserving transformations 37A35: Entropy and other invariants, isomorphism, classification 37A55: Relations with the theory of $C^*$-algebras 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations

Information

Type
Research Article
Information
Compositio Mathematica , Volume 157 , Issue 10 , October 2021 , pp. 2160 - 2198
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Copyright
© 2021 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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Footnotes

The author gratefully acknowledges support from NSF Grants DMS-1827376 and DMS-2000105.

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