{"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":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-06-25","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\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-06-25\",\"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\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000813\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021782424000813","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","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 .
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