The method of noncommutative integration for linear differential equations. Functional algebras and noncommutative dimensional reduction

Geometric theory, characteristics, transformations in context of PDEs (35A30) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72) Quadratic algebras (but not quadratic Jordan algebras) (17A45)

Related Items (8)

Algebras of symmetry operators of the Klein-Gordon-Fock equation for groups acting transitively on two-dimensional subspaces of a space-time manifold ⋮ Algebras of integrals of motion for the Hamilton–Jacobi and Klein–Gordon–Fock equations in spacetime with four-parameter groups of motions in the presence of an external electromagnetic field ⋮ Vacuum polarization of a scalar field on Lie groups and homogeneous spaces ⋮ Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions ⋮ Noncommutative integration and symmetry algebra of the Dirac equation on the Lie groups ⋮ Noncommutative integration of the Klein-Gordon equation in electromagnetic fields admitting functional arbitrariness ⋮ Scalar field vacuum polarization on homogeneous spaces with an invariant metric ⋮ Integrable \(N\)-dimensional systems on the Hopf algebra and \(q\)-deformations

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