The Looijenga-Lunts-Verbitsky Algebra and Verbitsky's Theorem

Alessio Bottini

doi:10.1007/s00032-022-00364-z

The Looijenga-Lunts-Verbitsky Algebra and Verbitsky's Theorem

Milan J Math. 2022;90(2):403-416. doi: 10.1007/s00032-022-00364-z. Epub 2022 Oct 3.

Author

Alessio Bottini^{1

2}

Affiliations

¹ Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy.
² Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d'Orsay, Rue Michel Magat, Bat. 307, 91405 Orsay, France.

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.