Integrable coupling of the Ablowitz–Ladik hierarchy and its Hamiltonian structure

The trace identity is generalized to work for the discrete zero-curvature equation associated with the Lie algebra possessing degenerate Killing forms. Then a kind of integrable coupling of the Ablowitz–Ladik (AL) hierarchy is obtained and its Hamiltonian structure is worked out. Moreover, Liouville integrability of the integrable coupling is demonstrated.