Lie symmetries of multidimensional difference equations

A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformati ons act on the equations and on the lattice. They take solutions into solut ions and can be used to perform symmetry reduction. The method generalizes the one presented in a recent publication for the case of ordinary differen ce equations. In turn, it can easily be generalized to difference systems i nvolving an arbitrary number of dependent and independent variables.