A multi-component matrix loop algebra and a unified expression of the multi-component AKNS hierarchy and the multi-component BPT hierarchy

A set of multi-component matrix Lie algebra is constructed, which is devote to obtaining a new loop algebra A˜M−1. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the bi-Hamiltonian structures. As its reduction cases, the multi-component AKNS hierarchy and the formalism of the multi-component BPT hierarchy are given, respectively.