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

The classification of differential-difference equations of the form u(nm) = F-nm(t, {upq}|((p,q)is an element of Gamma)) is considered according to their Lie point symmetry groups. The set Gamma 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.