Journal of Lie Theory 17 (2007), No. 4, 685--708
Copyright Heldermann Verlag 2007
Actions of R.widetilde(SL2R) on Laguerre Planes Related to the Moulton Planes
Rainer Löwen
Institut fuer Analysis und Algebra, Technische Universitaet, Pockelsstr. 14, 38106 Braunschweig, Germany
r.loewen@tu-bs.de
Günter F. Steinke
Dept. of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8020, New Zealand
G.Steinke@math.canterbury.ac.nz
We construct flat Laguerre planes that admit the universal covering group of SL2R, extended by a factor R, as a group of automorphisms. These planes contain the affine Moulton planes as derived planes, and they are constructed by gluing together two copies of a Moulton plane, folded up along their fixed lines. The action of the Moulton group carries over (modulo Z2) to the Laguerre planes, and the circles and parallel classes are essentially orbits of 4 types of one-parameter groups of the Moulton action. These planes have group dimension 4 and also provide examples of flat Laguerre planes of Kleinewillinghöfer type II.G.1.
Keywords: Universal cover of the unimodular group, Moulton plane, Moulton group, Laguerre plane.
MSC: 51H15, 51B15, 22E46
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