Differential symmetry algebras for linear homogeneous differential equations
type: Item
instance of: scholarly article
title: Differential symmetry algebras for linear homogeneous differential equations
zbMATH Open document ID: 1004.58512
author: A. I. Fomin
published in: Russian Journal of Mathematical Physics
publication date: 2003-01-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 58J70
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 1208152
zbMATH Keywords: internal symmetry
zbMATH Keywords: external symmetry
zbMATH Keywords: symmetry algebras
reviewed by: Michal Marvan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1208152