A new discrete integrable system and its discrete integrable coupling system

In terms of the properties of the known loop algebra A∼1 and difference operators, a new algebraic system X   is constructed, which is devote to working out the well-known generalized cubic Volterra lattice equations hierarchy. Then an extended algebraic system X∼ of X is presented, from which the integrable coupling system of generalized cubic Volterra lattice equations are obtained.