Continuous symmetries of equations on lattices

A method is presented for calculating the Lie point symmetries of difference equations with one, or several, independent variables. The equations are given on a priori specified lattices. The Lie transformations act on the lattice, as well as on the equation. The transformations take solutions into solutions and can be used to perform symmetry reduction. Presented by P. Winternitz at the DI-CRM Workshop held in Prague, 18–21 June 2000. This article was written while S.T. and P.W. were visiting the Dipartimento di Fisica, Università di Roma Tre. They thank the Dipartimento, the INFN and the Agreement Università di Roma Tre — Université de Montréal for their support. The research of P.W. was partly supported by a research grant from NSERC of Canada.