Noncommutative integration of linear differential equations

A method of noncommutative integration of linear partial differential equations that is analogous to noncommutative integration of finite-dimensional Hamiltonian systems is proposed. The method is based on the concept, introduced in the paper, of a $\lambda$ representation of Lie algebras. The method can be applied to the integration of the Klein–Gordon equation in Riemannian spaces of non-Stäckel type (i. e., in spaces that do not admit complete separation of the variables).