In mathematics, a jet group is a generalization of the general linear group which applies to Taylor polynomials instead of vectors at a point.
The k-th order jet group Gnk consists of jets of smooth diffeomorphisms φ: Rn → Rn such that φ(0)=0.
Similarly, derivatives of order up to m are sections of the jet bundle Jm(Rk) = Rk × W, where Here R* is the dual vector space to R, and Si denotes the i-th symmetric power.
There is a unique polynomial fp in k variables and of order m such that p is in the image of jmfp.
The differential data x′ may be transferred to lie over another point y ∈ Rn as jmfp(y) , the partials of fp over y.
Because of the properties of jets under function composition, Gnk is a Lie group.
It is also in fact an algebraic group, since the composition involves only polynomial operations.