Vol. 2, No. 1, 2005

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A note on Laguerre translations

Günter F. Steinke

Vol. 2 (2005), No. 1, 93–100
DOI: 10.2140/iig.2005.2.93
Abstract

Using the correspondence between 2n-dimensional Laguerre planes and compact antiregular generalized quadrangles with parameter n = 1,2 we show that almost each automorphism of such a Laguerre plane that induces a translation in the derived affine plane at a point p is a Laguerre translation, that is, fixes all points on the parallel class of p. The same is true for ovoidal Laguerre planes over ovals that also are dual ovals.

Keywords
Laguerre plane, Lie geometry, generalized quadrangle, Laguerre translation
Mathematical Subject Classification 2000
Primary: 51B15, 51H15
Milestones
Received: 8 April 2005
Accepted: 23 June 2005
Authors
Günter F. Steinke
School of Mathematics and Statistics
University of Canterbury
Private Bag 4800
Christchurch 8140
New Zealand