The Looijenga–Lunts–Verbitsky Algebra and Verbitsky’s Theorem

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...

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Detalles Bibliográficos
Autor principal: Bottini, Alessio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708818/
https://www.ncbi.nlm.nih.gov/pubmed/36466320
http://dx.doi.org/10.1007/s00032-022-00364-z
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author Bottini, Alessio
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description 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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spelling pubmed-97088182022-12-01 The Looijenga–Lunts–Verbitsky Algebra and Verbitsky’s Theorem Bottini, Alessio Milan J Math Article 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. Springer International Publishing 2022-10-03 2022 /pmc/articles/PMC9708818/ /pubmed/36466320 http://dx.doi.org/10.1007/s00032-022-00364-z Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Bottini, Alessio
The Looijenga–Lunts–Verbitsky Algebra and Verbitsky’s Theorem
title The Looijenga–Lunts–Verbitsky Algebra and Verbitsky’s Theorem
title_full The Looijenga–Lunts–Verbitsky Algebra and Verbitsky’s Theorem
title_fullStr The Looijenga–Lunts–Verbitsky Algebra and Verbitsky’s Theorem
title_full_unstemmed The Looijenga–Lunts–Verbitsky Algebra and Verbitsky’s Theorem
title_short The Looijenga–Lunts–Verbitsky Algebra and Verbitsky’s Theorem
title_sort looijenga–lunts–verbitsky algebra and verbitsky’s theorem
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708818/
https://www.ncbi.nlm.nih.gov/pubmed/36466320
http://dx.doi.org/10.1007/s00032-022-00364-z
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