{"title":"2 期 $$L_infty $ - 算法的分类","authors":"Kevin van Helden","doi":"10.1007/s40062-024-00354-5","DOIUrl":null,"url":null,"abstract":"<div><p>We classify all 2-term <span>\\(L_\\infty \\)</span>-algebras up to isomorphism. We show that such <span>\\(L_\\infty \\)</span>-algebras are classified by a Lie algebra, a vector space, a representation (all up to isomorphism) and a cohomology class of the corresponding Lie algebra cohomology.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-024-00354-5.pdf","citationCount":"0","resultStr":"{\"title\":\"Classification of 2-term \\\\(L_\\\\infty \\\\)-algebras\",\"authors\":\"Kevin van Helden\",\"doi\":\"10.1007/s40062-024-00354-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We classify all 2-term <span>\\\\(L_\\\\infty \\\\)</span>-algebras up to isomorphism. We show that such <span>\\\\(L_\\\\infty \\\\)</span>-algebras are classified by a Lie algebra, a vector space, a representation (all up to isomorphism) and a cohomology class of the corresponding Lie algebra cohomology.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40062-024-00354-5.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-024-00354-5\",\"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/s40062-024-00354-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We classify all 2-term \(L_\infty \)-algebras up to isomorphism. We show that such \(L_\infty \)-algebras are classified by a Lie algebra, a vector space, a representation (all up to isomorphism) and a cohomology class of the corresponding Lie algebra cohomology.
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