Journal of Lie Theory 23 (2013), No. 3, 885--897
Copyright Heldermann Verlag 2013
The Group Structure for Jet Bundles over Lie Groups
Cornelia Vizman
Dept. of Mathematics, West University of Timisoara, Bd. V. Parvan 4, 300223 Timisoara, Romania
vizman@math.uvt.ro
[Abstract-pdf]
\def\g{{\frak g}} The jet bundle $J^kG$ of $k$-jets of curves in a Lie group $G$ has a natural Lie group structure. We present an explicit formula for the group multiplication in the right trivialization and for the group 2-cocycle describing the abelian Lie group extension $\g\to J^{k}G\to J^{k-1}G$.
Keywords: Jet bundle, group cocycle, ordered partition, Leibniz algebra, near-ring.
MSC: 58A20, 20K35, 05A18
[ Fulltext-pdf (326 KB)] for subscribers only.