Symmetries of differential-difference dynamical systems in a two-dimensional lattice

The classification of differential-difference equations of the form u-ddotnm(t,{upq} (p,q) element of Γ) is considered according to their Lie point symmetry groups. The set Γ represents the point (n, m) and its six nearest neighbors in a two-dimensional triangular lattice. It is shown that the symmetry group can be at most 12 dimensional for Abelian symmetry algebras and 13 dimensional for nonsolvable symmetry algebras.