Jet group

Jet group

In mathematics, a jet group is a generalization of the general linear group which applies to Taylor polynomials instead of vectors at a point. Essentially a jet group describes how a Taylor polynomial transforms under changes of coordinate systems (or, equivalently, diffeomorphisms).

The "k"-th order jet group "G""n""k" consists of jets of smooth diffeomorphisms :φ:R"n"→R"n" such that φ(0)=0. Because of the properties of jets under function composition, "G""n""k" is a Lie group. The jet group is a semidirect product of the general linear group and a connected, simply connected nilpotent Lie group. It is also in fact an algebraic group, since the composition involves only polynomial operations.


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