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## Kuga-Satake construction and cohomology of hyperkähler manifolds

Advances in Mathematics. 2019. Vol. 351. P. 275-295.
Kurnosov N., Soldatenkov A., Verbitsky M.

Let M be a simple hyperkähler manifold. Kuga-Satake
construction gives an embedding of H^2(M, C) into the
second cohomology of a torus, compatible with the Hodge
structure. We construct a torus T and an embedding of the
graded cohomology space H^•(M, C) → H^{•+l}(T, C) for some
l, which is compatible with the Hodge structures and the
Poincaré pairing. Moreover, this embedding is compatible
with an action of the Lie algebra generated by all Lefschetz
sl(2)-triples on M.