INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES
We introduce inner amenability for discrete probability-measure-preserving (p.m.p.) groupoids and investigate its basic properties, examples, and the connection with central sequences in the full group of the groupoid or central sequences in the von Neumann algebra associated with the groupoid. Amon...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2020-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509420000158/type/journal_article |
| _version_ | 1827994841225625600 |
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| author | YOSHIKATA KIDA ROBIN TUCKER-DROB |
| author_facet | YOSHIKATA KIDA ROBIN TUCKER-DROB |
| author_sort | YOSHIKATA KIDA |
| collection | DOAJ |
| description | We introduce inner amenability for discrete probability-measure-preserving (p.m.p.) groupoids and investigate its basic properties, examples, and the connection with central sequences in the full group of the groupoid or central sequences in the von Neumann algebra associated with the groupoid. Among other things, we show that every free ergodic p.m.p. compact action of an inner amenable group gives rise to an inner amenable orbit equivalence relation. We also obtain an analogous result for compact extensions of equivalence relations that either are stable or have a nontrivial central sequence in their full group. |
| first_indexed | 2024-04-10T04:47:14Z |
| format | Article |
| id | doaj.art-736a9926e95542b19d1104ee996b7c27 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:14Z |
| publishDate | 2020-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-736a9926e95542b19d1104ee996b7c272023-03-09T12:34:47ZengCambridge University PressForum of Mathematics, Sigma2050-50942020-01-01810.1017/fms.2020.15INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCESYOSHIKATA KIDA0https://orcid.org/0000-0003-0283-2575ROBIN TUCKER-DROB1Graduate School of Mathematical Sciences, The University of Tokyo, Komaba,Tokyo153-8914, Japan;Department of Mathematics, Texas A&M University, College Station, TX 77843, USA;We introduce inner amenability for discrete probability-measure-preserving (p.m.p.) groupoids and investigate its basic properties, examples, and the connection with central sequences in the full group of the groupoid or central sequences in the von Neumann algebra associated with the groupoid. Among other things, we show that every free ergodic p.m.p. compact action of an inner amenable group gives rise to an inner amenable orbit equivalence relation. We also obtain an analogous result for compact extensions of equivalence relations that either are stable or have a nontrivial central sequence in their full group.https://www.cambridge.org/core/product/identifier/S2050509420000158/type/journal_article37A2028D1546L10 |
| spellingShingle | YOSHIKATA KIDA ROBIN TUCKER-DROB INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES Forum of Mathematics, Sigma 37A20 28D15 46L10 |
| title | INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES |
| title_full | INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES |
| title_fullStr | INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES |
| title_full_unstemmed | INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES |
| title_short | INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES |
| title_sort | inner amenable groupoids and central sequences |
| topic | 37A20 28D15 46L10 |
| url | https://www.cambridge.org/core/product/identifier/S2050509420000158/type/journal_article |
| work_keys_str_mv | AT yoshikatakida inneramenablegroupoidsandcentralsequences AT robintuckerdrob inneramenablegroupoidsandcentralsequences |