{"title":"具有强固冯-诺依曼代数的直角库克斯特群的分类","authors":"","doi":"10.1016/j.matpur.2024.06.006","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>W</em> be a finitely generated right-angled Coxeter group with group von Neumann algebra <span><math><mi>L</mi><mo>(</mo><mi>W</mi><mo>)</mo></math></span>. We prove the following dichotomy: either <span><math><mi>L</mi><mo>(</mo><mi>W</mi><mo>)</mo></math></span> is strongly solid or <em>W</em> contains <span><math><mi>Z</mi><mo>×</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> as a subgroup. This proves in particular strong solidity of <span><math><mi>L</mi><mo>(</mo><mi>W</mi><mo>)</mo></math></span> for all non-hyperbolic Coxeter groups that do not contain <span><math><mi>Z</mi><mo>×</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"189 ","pages":"Article 103591"},"PeriodicalIF":2.3000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000813/pdfft?md5=7815ad0f570af89f7e83c33e2d0c0dea&pid=1-s2.0-S0021782424000813-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Classification of right-angled Coxeter groups with a strongly solid von Neumann algebra\",\"authors\":\"\",\"doi\":\"10.1016/j.matpur.2024.06.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <em>W</em> be a finitely generated right-angled Coxeter group with group von Neumann algebra <span><math><mi>L</mi><mo>(</mo><mi>W</mi><mo>)</mo></math></span>. We prove the following dichotomy: either <span><math><mi>L</mi><mo>(</mo><mi>W</mi><mo>)</mo></math></span> is strongly solid or <em>W</em> contains <span><math><mi>Z</mi><mo>×</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> as a subgroup. This proves in particular strong solidity of <span><math><mi>L</mi><mo>(</mo><mi>W</mi><mo>)</mo></math></span> for all non-hyperbolic Coxeter groups that do not contain <span><math><mi>Z</mi><mo>×</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>.</p></div>\",\"PeriodicalId\":51071,\"journal\":{\"name\":\"Journal de Mathematiques Pures et Appliquees\",\"volume\":\"189 \",\"pages\":\"Article 103591\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000813/pdfft?md5=7815ad0f570af89f7e83c33e2d0c0dea&pid=1-s2.0-S0021782424000813-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal de Mathematiques Pures et Appliquees\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000813\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/6/25 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal de Mathematiques Pures et Appliquees","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021782424000813","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/6/25 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
给定一个直角库克斯特群和相关的冯-诺依曼代数，我们展示了以下替代方案：是强实心的，或者是 。特别是，这意味着不包含的非双曲 Coxeter 群有一个强固的 von Neumann 代数。
Classification of right-angled Coxeter groups with a strongly solid von Neumann algebra
Let W be a finitely generated right-angled Coxeter group with group von Neumann algebra . We prove the following dichotomy: either is strongly solid or W contains as a subgroup. This proves in particular strong solidity of for all non-hyperbolic Coxeter groups that do not contain .
期刊介绍：
Published from 1836 by the leading French mathematicians, the Journal des Mathématiques Pures et Appliquées is the second oldest international mathematical journal in the world. It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.
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