English

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.

Keywords

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

R2 v1 2026-06-24T06:33:21.920Z