Symmetries of trivial systems of ODEs of mixed order Academic Article

abstract

• 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.

authors

• Zelenko, Igor

published proceedings

• DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS

author list (cited authors)

• Doubrov, B., & Zelenko, I.

citation count

• 1

complete list of authors

• Doubrov, Boris||Zelenko, Igor

publication date

• January 2014

publisher

• Elsevier  Publisher

published in

• Differential Geometry and Its Applications  Journal

keywords

• Flag Structures
• Graded Lie Algebras
• Ordinary Differential Equations
• Sternberg Prolongation
• Symmetry Algebras
• Tanaka Prolongation

Digital Object Identifier (DOI)

• 10.1016/j.difgeo.2013.10.008

start page

• 123

end page

• 143

volume

• 33

URL

• http://dx.doi.org/10.1016/j.difgeo.2013.10.008