Cohomology algebra of hyperk\"ahler manifolds is Frobenius algebra and the total Lie algebra of Lefschetz sl(2)-triples acting on it is so(4,b_2-2) by results of Loojenga-Lunts and Verbitsky. I will discuss the generalization of the classic Kuga-Satake construction which allows us to embed cohomology of hyperk\"ahler manifolds to cohomology of some complex torus which is morphism of Hodge structures (joint with M.Verbitsky and A.Soldatenkov). Also I will briefly explain some interesting corollaries.