  The transcendental Hodge lattice of a projective manifold $M$ is the smallest
Hodge substructure in $p$-th cohomology which contains all holomorphic
$p$-forms. We prove that the direct sum of all transcendental Hodge lattices
has a natural algebraic structure, and compute this algebra explicitly for a
hyperkahler manifold. As an application, we obtain a theorem about dimension of
a compact torus $T$ admitting a symplectic embedding to a hyperkahler manifold
$M$. If $M$ is generic in a $d$-dimensional family of deformations, then $\dim
T\geq 2^{[(d+1)/2]}$.
