Coboundaries of commuting Borel automorphisms
We show that if \(S\), \(T\) are two commuting automorphisms of a standard Borel space such that they generate a free Borel \(\mathbb{Z}^2\)-action then \(S\) and \(T\) do not have same sets of real valued bounded coboundaries. We also prove a weaker form of Rokhlin Lemma for Borel \(\mathbb{Z}^d\)-...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AGH Univeristy of Science and Technology Press
2021-09-01
|
| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol41/5/art/opuscula_math_4132.pdf |
| _version_ | 1818726970723139584 |
|---|---|
| author | Shrey Sanadhya |
| author_facet | Shrey Sanadhya |
| author_sort | Shrey Sanadhya |
| collection | DOAJ |
| description | We show that if \(S\), \(T\) are two commuting automorphisms of a standard Borel space such that they generate a free Borel \(\mathbb{Z}^2\)-action then \(S\) and \(T\) do not have same sets of real valued bounded coboundaries. We also prove a weaker form of Rokhlin Lemma for Borel \(\mathbb{Z}^d\)-actions. |
| first_indexed | 2024-12-17T22:06:40Z |
| format | Article |
| id | doaj.art-3cdaffcdbc03499fbac606f0f82b8d95 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-17T22:06:40Z |
| publishDate | 2021-09-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-3cdaffcdbc03499fbac606f0f82b8d952022-12-21T21:30:50ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742021-09-01415667683https://doi.org/10.7494/OpMath.2021.41.5.6674132Coboundaries of commuting Borel automorphismsShrey Sanadhya0The University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, Iowa 52242, USAWe show that if \(S\), \(T\) are two commuting automorphisms of a standard Borel space such that they generate a free Borel \(\mathbb{Z}^2\)-action then \(S\) and \(T\) do not have same sets of real valued bounded coboundaries. We also prove a weaker form of Rokhlin Lemma for Borel \(\mathbb{Z}^d\)-actions.https://www.opuscula.agh.edu.pl/vol41/5/art/opuscula_math_4132.pdfcoboundriesrokhlin lemmaborel \(\mathbb{z}^d\)-action |
| spellingShingle | Shrey Sanadhya Coboundaries of commuting Borel automorphisms Opuscula Mathematica coboundries rokhlin lemma borel \(\mathbb{z}^d\)-action |
| title | Coboundaries of commuting Borel automorphisms |
| title_full | Coboundaries of commuting Borel automorphisms |
| title_fullStr | Coboundaries of commuting Borel automorphisms |
| title_full_unstemmed | Coboundaries of commuting Borel automorphisms |
| title_short | Coboundaries of commuting Borel automorphisms |
| title_sort | coboundaries of commuting borel automorphisms |
| topic | coboundries rokhlin lemma borel \(\mathbb{z}^d\)-action |
| url | https://www.opuscula.agh.edu.pl/vol41/5/art/opuscula_math_4132.pdf |
| work_keys_str_mv | AT shreysanadhya coboundariesofcommutingborelautomorphisms |