A characterization of the semi-isometries of a Minkowski plane over a field K
type: Item
instance of: scholarly article
title: A characterization of the semi-isometries of a Minkowski plane over a field K
zbMATH Open document ID: 0547.51005
DOI: 10.1007/BF01918141
author: F. Radó
published in: Journal of Geometry
publication date: 1983-01-01T00:00:00Z
review text: This is a deep and beautiful result on the characterization of Lorentz transformations in the plane over a field. More precisely: Suppose that K is a field of characteristics \(\neq 2\), 3, 5 or that \(K=GF(5^ m), m>1\). Suppose moreover that \(\sigma:K^ 2\to K^ 2\) is a mapping preserving the Lorentz-Minkowski distance 1. Then \(\sigma\) must be a Lorentz transformation of \(K^ 2\) up to a translation and up to a monomorphism of the field K. In the proof of this theorem there was also used a computer in order to construct very special configurations needed. Beyond it the proof works with tools of Minkowski's geometry and algebra.
Mathematics Subject Classification ID: 51B20
zbMATH DE Number: 3872157
zbMATH Keywords: Lorentz transformations
reviewed by: Walter Benz
MaRDI profile type: Publication
cites work: Q3241211
cites work: On Isometries of Euclidean Spaces
cites work: A characterization of plane Lorentz transformations
cites work: A Beckman-Quarles type theorem for finite Desarguesian planes
cites work: A characterization of isometries of absolute planes
cites work: On the characterization of plane affine isometries
cites work: Zur Kennzeichnung von Lorentztransformationen in endlichen Ebenen
cites work: Zur Kennzeichnung der Lorentz-Transformationen
cites work: On a theorem by W. Benz characterizing plane Lorentz transformations in Jaernefelt's world
Recommended article: Q3689774
Recommended article: Q3814305
Recommended article: A remark on the characterization of semi-isometries over skewfields
Recommended article: A classification of Minkowski planes over half-ordered fields
Recommended article: A family of Minkowski planes over half-ordered fields
Recommended article: Q4966469
Recommended article: Q3764802
Recommended article: Q3319330
Recommended article: On the characterization of a semi-multiplicative analogue of planar functions over finite fields
Recommended article: Minkowski semi-planes
description: scientific article; zbMATH DE number 3872157