Symmetries of trivial systems of ODEs of mixed order Academic Article uri icon


  • We compute symmetry algebras of a system of two equations y(k)(x) = z(l)(x) = 0, where 2 k < l. It appears that there are many ways to convert such system of ODEs to an exterior differential system. They lead to different series of finite-dimensional symmetry algebras. For example, for (k, l) = (2, 3) we get two non-isomorphic symmetry algebras of the same dimension. We explore how these symmetry algebras are related to both Sternberg prolongation of G-structures and Tanaka prolongation of graded nilpotent Lie algebras.Surprisingly, the case (k, l) = (2, 3) provides an example of a linear subalgebra a in gl(5,R) such that the Sternberg prolongations of a and at are both of the same dimension, but are non-isomorphic.We also discuss the non-linear case and the link with flag structures on smooth manifolds. 2013 Elsevier B.V.

published proceedings


author list (cited authors)

  • Doubrov, B., & Zelenko, I.

citation count

  • 1

complete list of authors

  • Doubrov, Boris||Zelenko, Igor

publication date

  • January 2014