Extended curvatures and Lie pseudoalgebras

Abstract

The aim of the paper is to prove that if some extended curvatures on a preinfinitesimal module L, considered in the paper, vanish, then the derived preinfinitesimal module L(1) is a Lie pseudoalgebra. Two non-trivial examples are given. The first example is when L0 is an infinitesimal module and the second one is when L1 is a preinfinitesimal module.