# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Affine structures on jet and Weil bundles

### Tom 114 / 2009

Colloquium Mathematicum 114 (2009), 291-305 MSC: 58A20, 58A32. DOI: 10.4064/cm114-2-10

#### Streszczenie

Weil algebra morphisms 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 passes to jet spaces. We give a characterization of this fact in algebraic terms. This algebraic condition also determines an affine structure on the groups of automorphisms of related Weil algebras.

#### Autorzy

• David Blázquez-SanzEscuela de Matemáticas