Point-reflection geometries, geometric K-loops and unitary geometries
type: Item
instance of: scholarly article
title: Point-reflection geometries, geometric K-loops and unitary geometries
zbMATH Open document ID: 0922.51006
DOI: 10.1007/BF03322525
author: Elisabetta Gabrieli
author: Helmut Karzel
published in: Results in Mathematics
publication date: 1999-10-05T00:00:00Z
review text: The authors use unitary geometries to show the existence of reflection geometries to which correspond \(K\)-loops with an incidence fibration \(F\) [\textit{E. Zizioli}, J. Geom. 30, 144-156 (1987; Zbl 0632.51019)] where \(F\) consists of proper subloops (other than groups). This is in sharp contrast to ordinary hyperbolic spaces, where those subloops are even commutative subgroups.
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 1112237
zbMATH Keywords: loops
zbMATH Keywords: reflection structures
reviewed by: Hans Havlicek
MaRDI profile type: Publication
cites work: Zur Begründung der Geometrie aus dem Spiegelungsbegriff
cites work: Recent developments on absolute geometries and algebraization by K-loops
cites work: Reflection groups and \(K\)-loops
cites work: Q4271560
cites work: Die Dualität von Inzidenz und Senkrechtstehen in der absoluten Geometrie
cites work: Fibered indidence loops and kinematic loops
full work available at URL: https://doi.org/10.1007/bf03322525
OpenAlex ID: W2005523127
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description: scientific article; zbMATH DE number 1112237