Lagrangian Formalism Over Graded Algebras

Abstract

This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary first step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative version of integration procedure, the notion of adjoint operator, Green's formula, the relation between integral and differential forms, conservation laws, Euler operator, Noether's theorem is considered.Comment: 26 pages, AMS-TeX 2.1, to appear in J. Geom. Phys. (resubmitted because of a TeX-error