A direct extension of the known Lie algebra An-1 is presented, a new Lie algebra gl(n,C) is obtained. For the sake of application convenience, Lie algebra gl(3,C) is only considered, whose subalgebra is constructed. By the definition of the subalgebra gradation,a new loop algebra is shown. As its application, an isospectral problem is designed. It follows that a new Lax pair is obtained. By making use of Tu scheme, a family of new Liouville integrable system is resented, which possesses a biHamiltonian structure. As the reduction case of the hierarchy obtained, a new coupled generalized Schrdinger equation is obtained.
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