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Let M be a simple hyperkahler manifold. Kuga-Satake construction gives anembedding of H^2(M,C) into the second cohomology of a torus, compatible withthe Hodge structure. We construct a torus T and an embedding of the gradedcohomology space H^*(M,C) \to H^{*+l}(T,C) for some l, which is compatible withthe Hodge structures and the Poincare pairing. Moreover, this embedding iscompatible with an action of the Lie algebra generated by all Lefschetzsl(2)-triples on M.

Kuga-Satake construction and cohomology of hyperkahler manifolds