{"title":"Lamplier李代数的同调","authors":"Y. Félix, A. Murillo","doi":"10.1007/s10469-022-09668-w","DOIUrl":null,"url":null,"abstract":"<div><div><p>It is proved that the associated Lie algebra of the Mal’tsev ℚ-completion of the lamplighter group is the pronilpotent completion of the lamplighter Lie algebra. It is also shown that the homology of this completed Lie algebra is of uncountable dimension in each degree.</p></div></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The Homology of the Lamplighter Lie Algebra\",\"authors\":\"Y. Félix, A. Murillo\",\"doi\":\"10.1007/s10469-022-09668-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div><p>It is proved that the associated Lie algebra of the Mal’tsev ℚ-completion of the lamplighter group is the pronilpotent completion of the lamplighter Lie algebra. It is also shown that the homology of this completed Lie algebra is of uncountable dimension in each degree.</p></div></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10469-022-09668-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10469-022-09668-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is proved that the associated Lie algebra of the Mal’tsev ℚ-completion of the lamplighter group is the pronilpotent completion of the lamplighter Lie algebra. It is also shown that the homology of this completed Lie algebra is of uncountable dimension in each degree.
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