Point-Reflection Geometries, Geometric K-Loops and Unitary Geometries

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 1997 English Publisher:Springer Science and Business Media LLCJournal:Results in Mathematics, volume 32, pages 66-72 (issn: 1422-6383, eissn: 1420-9012,

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Authors: Gabrieli, Elisabetta; Karzel, Helmut;

doi: 10.1007/bf03322525

Point-Reflection Geometries, Geometric K-Loops and Unitary Geometries

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Abstract

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.

Related Organizations

Catholic University of the Sacred Heart
Italy
Technical University of Munich
Germany
Universidad Católica de Cuyo
Argentina

Keywords

Loops, quasigroups, loops, Reflection groups, reflection geometries, reflection structures

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