
Journal of Lie Theory 17 (2007), No. 4, 685708 Copyright Heldermann Verlag 2007 Actions of R.widetilde(SL_{2}R) on Laguerre Planes Related to the Moulton Planes Rainer Löwen Institut fuer Analysis und Algebra, Technische Universitaet, Pockelsstr. 14, 38106 Braunschweig, Germany r.loewen@tubs.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 SL_{2}R, 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 Z_{2}) to the Laguerre planes, and the circles and parallel classes are essentially orbits of 4 types of oneparameter 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 [ Fulltextpdf (228 KB)] 