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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 T≥ 2^[(d+1)/2].arXiv:1512.01011v3 fatcat:2a7rcdqq6nciblwscms3el6zmq