On Differential form Method to Find Lie Symmetries of two Types of Toda Lattices

In this paper, we investigate Lie symmetries of the (1 + 1)-dimensional celebrated Toda lattice and the (2 + 1)-dimensional modified semidiscrete Toda lattice by using the extended Harrison and Estabrook's geometric approach. Two closed ideals written in terms of a set of differential forms are constructed for Toda lattices. Moreover, commutation relations of a Kac–Moody–Virasoro type Lie algebra are obtained by direct computation.