A new Lie algebra, a corresponding multi-component integrable hierarchy and an integrable coupling

A new simple loop algebra is constructed, which is devote to establishing an isospectral problem. By making use of Tu scheme, a new multi-component integrable hierarchy is obtained. Again via expanding the loop algebra above, another higher-dimensional loop algebra is presented. It follows that the binary integrable coupling systems are given. This method proposed in this paper can be used to other soliton hierarchies.