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Journal of Lie Theory 11 (2001), No. 2, 415--426
Copyright Heldermann Verlag 2001

Characterization of the Kantor-Koecher-Tits Algebra by a Generalized Ahlfors Operator

Wolfgang Bertram
Institut Elie Cartan, Université Nancy I, 54506 Vandoevre lès Nancy, France

Joachim Hilgert
Institute of Mathematics, Technical University, Erzstr. 1, 38678 Clausthal-Zellerfeld, Germany

In the context of certain generalized conformal structures we define a first order differential operator S generalizing the classical Ahlfors operator. We prove its invariance under the corresponding conformal group and show that, under certain conditions, the Lie algebra of this group (which is also known as the "Kantor-Koecher-Tits algebra") is precisely the space of solutions of the differential equation SX = 0.

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