Algebraic approach to the study of quantum integrability

The basic problem of quantum integrability has been systematically studied with an algebraic approach. With the introduction of the dynamical symmetry algebra the difficulty in transferring the classical integrability conditi on into (quantum mechanics is resolved. Using the superconvergent technique of Kolmogorov, it has been proved that systems with Hamiltonians expressed merely with elements of a definite dynamical symmetry algebra form an inte grable class of systems corresponding to that dynamical symmetry.