Differential symmetry algebras for linear homogeneous differential equations
The paper deals with symmetry algebras of systems of linear homogeneous (in particular, differential) equations \(P_\gamma = 0\), \(\gamma \in \Gamma\). Besides of internal symmetries or symmetries that reflect only the structure of the left ideal generated by the operators \(P_\gamma\), considered are also external symmetries or symmetries preserving a particular linear space of solutions. As the main result, criteria for the algebras of internal and external symmetries to coincide are given in terms of linear intermediate integrals and divisibility of linear operators. Treated in detail are ordinary linear differential equations and nondegenerate linear differential operators with analytic coefficients, in particular, elliptic ones.
scientific article; zbMATH DE number 1208152