A multi-component integrable hierarchy and its multi-component expanding integrable model

A set of multi-component matrix Lie algebra G1 is constructed, which is devoted to obtain a generalized loop algebra G∼1, then an isospectral problem is established. Specially in this paper, a new Lax multi-component integrable hierarchy containing an arbitrary positive integer M is obtained by choosing V with derivatives in x and spectral potentials. Then the multi-component expanding integrable model of the hierarchy obtained is presented by constructing the expanding loop algebra of G∼.