A new loop algebra and its subalgebras

The new concept of cycled numbers is proposed, from which a new loop algebra is properly constructed. Taking account of applicable needs, a few subalgebras of the loop algebras is presented. By employing one of the subalgebras and Tu scheme, a new integrable hierarchy of soliton equations with multi-component potential functions is worked out, which possesses bi-Hamiltonian structures. The method proposed in this paper can be used generally.