Journal of Lie Theory

no. 3
Higher Order Jet Bundles of Lie Group-Valued Functions
Journal of Lie Theory, Volume 33 (2023) no. 3, pp. 831-844
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.
DOI: 10.5802/jolt.1308
Classification: 22E30, 58A20, 22E60
Keywords: Fiber bundle, Lie groupoid, jet bundle, partition, tensor product 
@article{JOLT_2023_33_3_a7,
     author = {M. Castrill\~A3n L\~A3pez and A. Rodr\~A\-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},
     doi = {10.5802/jolt.1308},
     zbl = {1537.22020},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1308/}
}
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%0 Journal Article
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%A A. Rodríguez Abella
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%J Journal of Lie Theory
%D 2023
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M. CastrillÃ3n LÃ3pez; A. Rodríguez Abella. Higher Order Jet Bundles of Lie Group-Valued Functions. Journal of Lie Theory, Volume 33 (2023) no. 3, pp. 831-844. doi: 10.5802/jolt.1308

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