Higher order relations of the Plucker embedding of Grasmannian 2,n A.Khoroshkin We apply the theory of Lie algebra cohomologies for the calculations of the spaces of syzygies of arbitrary projective quadratic embeddings ( i.e. the space of equations, the relations between equations, the relations between relations and so on). As an illustration we calculate syzygies of the Plucker embedding of the Grasmannian of 2-dimensional planes.