Abstract
AbstractWeil algebra morphism induce natural transformations between Weilbundles. In some well known cases, a natural transformation is endowedwith a canonical structure of affine bundle. We show that this structurearises only when the Weil algebra morphism is surjective and its kernelhas null square. Moreover, in some cases, this structure of affine bundleis passed down to Jet spaces. We give a characterization of this factin algebraic terms. This algebraic condition also determines an affinestructure between the groups of automorphisms of related Weil algebras. Mathematical Subject Classification 58A20, 58A32Key Words:Jet, Weil Bundles, Affine Structure, Natural Transformations. Introduction The theory of Weil bundles and Jet spaces is developed in order to understandthe geometry of PDE systems. C. Ehresmann formalized contact elements of S.Lie, introducing the spaces of jets of sections; simultaneously A. Weil showed in[8] that the theory of S. Lie could be formalized easily by replacing the spacesof contact elements by the more formal spaces of
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