Symmetries of the discrete nonlinear Schrodinger equation

The Lie algebra L(h) of point symmetries of a discrete analogue of the nonl inear 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 b oth point and generalized symmetries, transforms into the hire-dimensional point symmetry algebra of the NLS.