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Letters in Mathematical Physics

, Volume 29, Issue 2, pp 151–163 | Cite as

On the relation between weak and strong invariance of differential equations

  • José F. Cariñena
  • M. A. Del Olmo
  • P. Winternitz
Article

Abstract

Some concepts of Lie algebra cohomology are used to systematize the search for differential equations invariant under a given Lie groupG. In particular, it is shown that if a ‘strongly invariant’ equation exists, then all ‘weakly invariant’ equations differ from it only by an arbitrary multiplicative factor. If no ‘strongly invariant’ equation exists, then cohomology theory can be used to simplify the search for ‘weakly invariant’ equations.

Mathematics Subject Classifications (1991)

17B56 57T10 22Exx 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • José F. Cariñena
    • 1
  • M. A. Del Olmo
    • 2
  • P. Winternitz
    • 3
  1. 1.Departamento de Fisica TeóricaUniversidad de ZaragozaZaragozaSpain
  2. 2.Departamento de Fisica TeóricaUniversidad de ValladolidValladolidSpain
  3. 3.Centre de Recherches MathematiquesUniversité de MontréalMontréalCanada

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