The Liouville integrable systems associated with a new discrete 3×3 matrix spectral problem

A new discrete 3 times 3 matrix spectral problem with three potentials is introduced, and the corresponding family of Liouville integrable lattice equations is obtained by applying the discrete trace identity. It is shown that the hierarchy possesses a Hamiltonian structure and a hereditary recursion operator, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals. Finally, infinitely many conservation laws of corresponding lattice systems are obtained by a direct way.