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Partially bounded transformations have trivial centralizers


Authors: Johann Gaebler, Alexander Kastner, Cesar E. Silva, Xiaoyu Xu and Zirui Zhou
Journal: Proc. Amer. Math. Soc. 146 (2018), 5113-5127
MSC (2010): Primary 37A40; Secondary 37A05, 37A50
DOI: https://doi.org/10.1090/proc/14091
Published electronically: September 17, 2018
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Abstract: We prove that for infinite rank-one transformations satisfying a property called ``partial boundedness,'' the only commuting transformations are powers of the original transformation. This shows that a large class of infinite measure-preserving rank-one transformations with bounded cuts have trivial centralizers. We also characterize when partially bounded transformations are isomorphic to their inverse.


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Additional Information

Johann Gaebler
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email: johann.gaebler@gmail.com

Alexander Kastner
Affiliation: Department of Mathematics, Williams College, Williamstown, Massachusetts 01267
Email: kastneralexander9@gmail.com

Cesar E. Silva
Affiliation: Department of Mathematics, Williams College, Williamstown, Massachusetts 01267
Email: csilva@williams.edu

Xiaoyu Xu
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: xiaoyux@princeton.edu

Zirui Zhou
Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
Email: zirui_zhou@berkeley.edu

DOI: https://doi.org/10.1090/proc/14091
Keywords: Infinite measure-preserving, ergodic, rank-one, centralizer
Received by editor(s): June 30, 2017
Published electronically: September 17, 2018
Additional Notes: This paper is based on research done in the ergodic theory group of the 2016 SMALL research project at Williams College. Support for the project was provided by National Science Foundation grant DMS-1347804, the Science Center of Williams College, and the Williams College Finnerty Fund. We would like to thank Madeleine Elyze, Juan Ortiz Rhoton, and Vadim Semenov, the other members of the SMALL 2016 ergodic theory group, for useful discussions and continuing support.
Communicated by: Nimish Shah
Article copyright: © Copyright 2018 American Mathematical Society

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