7,411 research outputs found
Affine Structures on Jet and Weil Bundles
Weil algebra morphism induce natural transformations between Weil bundles. In
some well known cases, a natural transformation is endowed with a canonical
structure of affine bundle. We show that this structure arises only when the
Weil algebra morphism is surjective and its kernel has null square. Moreover,
in some cases, this structure of affine bundle is passed down to Jet spaces. We
give a characterization of this fact in algebraic terms. This algebraic
condition also determines an affine structure between the groups of
automorphisms of related Weil algebrasComment: 16 page
Parallelisms & Lie Connections
The aim of this article is to study rational parallelisms of algebraic
varieties by means of the transcendence of their symmetries. The nature of this
transcendence is measured by a Galois group built from the Picard-Vessiot
theory of principal connections
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