{"title":"The Looijenga-Lunts-Verbitsky Algebra and Verbitsky's Theorem.","authors":"Alessio Bottini","doi":"10.1007/s00032-022-00364-z","DOIUrl":null,"url":null,"abstract":"<p><p>In these notes we review some basic facts about the LLV Lie algebra. It is a rational Lie algebra, introduced by Looijenga-Lunts and Verbitsky, acting on the rational cohomology of a compact Kähler manifold. We study its structure and describe one irreducible component of the rational cohomology in the case of a compact hyperkähler manifold.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"90 2","pages":"403-416"},"PeriodicalIF":1.2000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708818/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Milan Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00032-022-00364-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2022/10/3 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In these notes we review some basic facts about the LLV Lie algebra. It is a rational Lie algebra, introduced by Looijenga-Lunts and Verbitsky, acting on the rational cohomology of a compact Kähler manifold. We study its structure and describe one irreducible component of the rational cohomology in the case of a compact hyperkähler manifold.
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