FACTORIZABLE LIE SYMMETRIES AND THE LINEARIZATION OF DIFFERENCE-EQUATIONS

We show that an autonomous difference equation, of arbitrary order and with one or more independent variables, can be linearized by a point transformation if and only if it admits a symmetry vector field whose coefficient function is the product of two functions, one of the depen dent variable u and one of the independent variables x: X(x, u) = A(x) G(u)partial derivative/partial derivative u . The factor depending on the independent variables, A, is required to satisfy some non-degenera cy conditions. This result is derived using a discrete jet space forma lism for partial and ordinary difference equations, analogous to that used for the study of differential equations.