The Looijenga-Lunts-Verbitsky algebra and Verbitsky's Theorem
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\"ahler manifold. We study its structure and describe one irreducible component of the rational cohomology in the case of a compact hyperk\"ahler manifold.
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