INFINITE DIMENSIONAL LIE ALGEBRA COHOMOLOGY AND THE
COHOMOLOGY OF INVARIANT EULER-LAGRANGE COMPLEXES:
A PRELIMINARY REPORT

Juha Pohjanpelto and Ian M. Anderson

Key words: Inverse problem of calculus of variations, group actions,
        Lie algebra cohomology.

1991 Math. Subject Classification: 49N45, 58E30, 58G35.

Abstract: Let $\pi\:E\to M$ be a fiber bundle and let
$G$ be an infinite dimensional  Lie  pseudo-group of projectable
transformations acting on $E$.
We outline a general method by which the local cohomology of the $G$
invariant Euler-Lagrange complex on $E$ can be  computed in terms of
the Lie algebra cohomology of the formal infinitesimal generators
of $G$. Our method is illustrated with two examples.