Lagrangian supersymmetries depending on derivatives. Global analysis and cohomology

Abstract

Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in a very general setting. The cohomology of the variational bicom- plex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed. In particular, the first variational formula and conservation laws for Lagrangian systems on graded manifolds using contact supersym- metries are obtained