The Looijenga-Lunts-Verbitsky algebra and Verbitsky's Theorem
Algebraic Geometry
2021-10-04 v1
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 K\"{a}hler manifold. We study its structure and describe one irreducible component of the rational cohomology in the case of a compact hyperk\"{a}hler manifold.
Cite
@article{arxiv.2110.00419,
title = {The Looijenga-Lunts-Verbitsky algebra and Verbitsky's Theorem},
author = {Alessio Bottini},
journal= {arXiv preprint arXiv:2110.00419},
year = {2021}
}
Comments
This review was prepared in the context of the seminar organized by the ERC Synergy Grant HyperK