Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, 28040 Madrid, Spain Eduardo_Aguirre@Mat.UCM.Es
Departamento de Geometria y Topologia, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain email@example.com
Abstract: The 3-jet lift $G^3$ of a matrix group $G$ is isomorphic, via a map that we give explicitly, to a semidirect product of $G$ itself and a nilpotent group builded up from the first two prolongations of its Lie algebra. Using this isomorphism, we write down the formulas for the most natural representations of $G^3$, as well as for one additional representation of the 2-jet lift $G^2$ appearing when $G$ is of finite type 2. We apply these results to the case of the (linear) conformal group and we point out the geometric implications of these representations.
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