{"title":"关于Torelli Lie代数","authors":"A. Kupers, O. Randal-Williams","doi":"10.1017/fmp.2023.10","DOIUrl":null,"url":null,"abstract":"Abstract We prove two theorems about the Malcev Lie algebra associated to the Torelli group of a surface of genus g: Stably, it is Koszul and the kernel of the Johnson homomorphism consists only of trivial \n$\\mathrm {Sp}_{2g}(\\mathbb {Z})$\n -representations lying in the centre.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On the Torelli Lie algebra\",\"authors\":\"A. Kupers, O. Randal-Williams\",\"doi\":\"10.1017/fmp.2023.10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove two theorems about the Malcev Lie algebra associated to the Torelli group of a surface of genus g: Stably, it is Koszul and the kernel of the Johnson homomorphism consists only of trivial \\n$\\\\mathrm {Sp}_{2g}(\\\\mathbb {Z})$\\n -representations lying in the centre.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2021-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/fmp.2023.10\",\"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://doi.org/10.1017/fmp.2023.10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Abstract We prove two theorems about the Malcev Lie algebra associated to the Torelli group of a surface of genus g: Stably, it is Koszul and the kernel of the Johnson homomorphism consists only of trivial
$\mathrm {Sp}_{2g}(\mathbb {Z})$
-representations lying in the centre.
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