Einbettung gewisser Kettengeometrien in projektive Räume

verfasst von

Herbert Hotje

Abstract

The theory of "chain geometries" as represented in [2] is a generalisation of the concept of Möbius-, Laguerre- and pseudo-euclidean planes over a commutative field K. It is well known that these geometries can be represented as a 2-dimensional variety of the 3-dimensional projective space over K. It will be shown how to embed in a similar way a class of "chain geometries", which covers these planes. The algebras belonging to these geometries are the kinematic algebras, studied by H.KARZEL, in which x²∃ Kx+K for each element x of the algebra. If the algebra is of rank n the geometry will be represented on a n-dimensional algebraic variety of the (n+1)-dimensional projective space π, the chains being the intersection of with planes of π having no line but at least two points in common with.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Journal of Geometry

Band

5

Seiten

85-94

Anzahl der Seiten

10

ISSN

0047-2468

Publikationsdatum

03.1974

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Geometrie und Topologie

Elektronische Version(en)

https://doi.org/10.1007/BF01954538 (Zugang: Geschlossen)