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Journal of Lie Theory, Vol. 11, No. 2, pp. 415-426 (2001)
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#
Characterization of the Kantor-Koecher-Tits Algebra by a Generalized Ahlfors Operator

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Wolfgang Bertram and Joachim Hilgert

Institut Elie Cartan

Université Nancy I

B.P. 239

F-54506 Vandoeuvre lès Nancy, Cedex

France

email: bertram@iecn.u-nancy.fr

and

Institut für Mathematik

TU Clausthal

Erzstr. 1

D-38678 Clausthal-Zellerfeld

Germany

email: hilgert@math.tu-clausthal.de

**Abstract:** 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 $SX=0$.

**Full text of the article:**

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