  Let M be a simple hyperkahler 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) \to H^{*+l}(T,C) for some l, which is compatible with
the Hodge structures and the Poincare pairing. Moreover, this embedding is
compatible with an action of the Lie algebra generated by all Lefschetz
sl(2)-triples on M.
