A Lie algebra attached to a projective variety

@article{Looijenga1997ALA,
  title={A Lie algebra attached to a projective variety},
  author={Eduard Looijenga and Valery Lunts},
  journal={Inventiones mathematicae},
  year={1997},
  volume={129},
  pages={361-412}
}
A bstract . Each choice of a Kähler class on a compact complex manifold defines an action of the Lie algebra sl(2) on its total complex cohomology. If a nonempty set of such Kähler classes is given, then we prove that the corresponding sl(2)-copies generate a semisimple Lie algebra. We investigate the formal properties of the resulting representation and we work things out explicitly in the case of complex tori, hyperkähler manifolds and flag varieties. We pay special attention to the cases… CONTINUE READING

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