Journal of Lie Theory, Vol. 11, No. 2, pp. 415-426 (2001)

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

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 $SX=0$.

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