Symmetries of the discrete nonlinear Schrodinger equation

The Lie algebra L(h) of point symmetries of a discrete analogue of the nonlinear Schrodinger equation (NLS) is described. In the continuous limit, the discrete equation is transformed into the NLS, while the structure of the Lie algebra changes: a contraction occurs with the lattice spacing h as the contraction parameter. A live-dimensional subspace of L(h), generated by both point and generalized symmetries, transforms into the hire-dimensional point symmetry algebra of the NLS.