On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms

Günter F. Steinke

Type: Article

Publication Date: 1999-01-15

Citations: 4

DOI: https://doi.org/10.1515/form.11.1.79

Abstract

This paper concerns 4-dimensional (topological locally compact connected) elation Laguerre planes that admit large automorphism groups. In particular, it is shown that such a plane is classical if its automorphism group is at least 11-dimensional. Furthermore, the elation Laguerre planes admitting simple Lie groups of automorphisms are investigated and various characterizations of the classical complex Laguerre plane and the semi-classical Laguerre planes are obtained.

Locations

UC Research Repository (University of Canterbury) - View - PDF
Forum Mathematicum - View

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Action	Title	Year	Authors
+	A classification of 4-dimensional elation Laguerre planes of group dimension 10	2006	Günter F. Steinke
+	Sisters of some 4-dimensional elation Laguerre planes of group dimension 10	2009	Günter F. Steinke
+	A Characterization of Certain Elation Laguerre Planes in Terms of Kleinewillinghöfer Types	2009	Günter F. Steinke
+	A note on the Kleinewillinghöfer types of 4-dimensional Laguerre planes	2022	Günter F. Steinke

Works Cited by This (23)

Action	Title	Year	Authors
+ PDF Chat	Tabellen zu den einfachen Lie Gruppen und ihren Darstellungen	1967	Jacques Tits
+	Topological Circle Planes and Topological Quadrangles	1995	Andreas E. Schroth
+ PDF Chat	Geometric $ABA$-groups	1961	D. G. Higman J. E. McLaughlin
+	Finite Generalized Quadrangles	2009	Stanley E. Payne J. A. Thas
+	4-dimensionale Translationsebenen mit 8-dimensionaler Kollineationsgruppe	1973	Dieter Betten
+	Topological pseudo-ovals, elation laguerre planes, and elation generalized quadrangles	1994	Rainer Löwen
+	Semiclassical 4-dimensional Laguerre Planes	1990	Günter F. Steinke
+	Dimension der Bahnen lokal kompakter Gruppen	1971	Heinz-Richard Halder
+	Kollineationsgruppen kompakter 4-dimensionaler Ebenen. II	1971	Helmut Salzmann
+	Kompakte, vier-dimensionale projektive Ebenen mit 8-dimensionaler Kollineationsgruppe	1973	Helmut Salzmann