Abstract
By introducing two specific matrix spectral problems associated with sl(2, R) and so(3, R) matrix Lie algebras, we generate two integrable Hamiltonian hierarchies with three potentials. The computation and analysis on their Hamiltonian structures by means of the trace identity show that the resulting hierarchies are Liouville integrable, namely, that each hierarchy consists of commuting Hamiltonian soliton equations. Published by AIP Publishing.