Affine structures on jet and Weil bundles

David Blázquez-Sanz. "Affine structures on jet and Weil bundles." Colloquium Mathematicae 114.2 (2009): 291-305. <http://eudml.org/doc/284296>.

@article{DavidBlázquez2009,
abstract = {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.},
author = {David Blázquez-Sanz},
journal = {Colloquium Mathematicae},
keywords = {Weil bundles; jet bundles; affine structure; natural transformation},
language = {eng},
number = {2},
pages = {291-305},
title = {Affine structures on jet and Weil bundles},
url = {http://eudml.org/doc/284296},
volume = {114},
year = {2009},
}

TY - JOUR
AU - David Blázquez-Sanz
TI - Affine structures on jet and Weil bundles
JO - Colloquium Mathematicae
PY - 2009
VL - 114
IS - 2
SP - 291
EP - 305
AB - 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.
LA - eng
KW - Weil bundles; jet bundles; affine structure; natural transformation
UR - http://eudml.org/doc/284296
ER -