A general method for generating multicomponent integrable hierarchies

A Lie algebra, whose bases are the forms of M × 3 matrices, is defined. Subsequently two types of loop algebras are constructed, whose commutative operations are equivalent to known ones proposed before. By using the Tu scheme, the mulicomponent KN hierarchy and its integrable coupling system, as well as a generalized multicomponent AKNS integrable hierarchy with five potential functions are obtained. The procedure presented in this paper is simple and straightforward and can be used generally