A new matrix Lie algebra, the multicomponent Yang hierarchy and its super-integrable coupling system

A set of new matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A∼2M. It follows that an isospectral problem is established. By use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the multi-component Hamiltonian structures. As its reduction cases, the multi-component Yang hierarchy is given. Finally, the multi-component super-integrable coupling system of Yang hierarchy is presented by enlarging matrix spectral problem.