For each positive integer $k$, the bundle of $k$-jets of functions from a smooth manifold, $X$, to a Lie group, $G$, is denoted by $J^k(X,G)$ and it is canonically endowed with a Lie groupoid structure over $X$. In this work, we utilize a linear connection to trivialize this bundle, i.e., to build an injective bundle morphism from $J^k(X,G)$ into a vector bundle over $G$. Afterwards, we give the explicit expression of the groupoid multiplication on the trivialized space, as well as the formula for the inverse element. In the last section, a coordinated chart on $X$ is considered and the local expression of the trivialization is computed.
Marco Castrillón López
1
;
Álvaro Rodríguez Abella
2
1
Facultad de Ciencias Matemáticas, Universidad Complutense, Madrid, Spain
2
Instituto de Ciencias Matemáticas, Madrid, Spain
Marco Castrillón López; Álvaro Rodríguez Abella. Higher Order Jet Bundles of Lie Group-Valued Functions. Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 831-844. http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a7/
@article{JOLT_2023_33_3_a7,
author = {Marco Castrill\'on L\'opez and \'Alvaro Rodr{\'\i}guez Abella},
title = {Higher {Order} {Jet} {Bundles} of {Lie} {Group-Valued} {Functions}},
journal = {Journal of Lie Theory},
pages = {831--844},
year = {2023},
volume = {33},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a7/}
}
TY - JOUR
AU - Marco Castrillón López
AU - Álvaro Rodríguez Abella
TI - Higher Order Jet Bundles of Lie Group-Valued Functions
JO - Journal of Lie Theory
PY - 2023
SP - 831
EP - 844
VL - 33
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a7/
ID - JOLT_2023_33_3_a7
ER -
%0 Journal Article
%A Marco Castrillón López
%A Álvaro Rodríguez Abella
%T Higher Order Jet Bundles of Lie Group-Valued Functions
%J Journal of Lie Theory
%D 2023
%P 831-844
%V 33
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a7/
%F JOLT_2023_33_3_a7
