Einbettung gewisser Kettengeometrien in projektive Räume

authored by: 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.
Organisation(s): Institute of Algebra, Number Theory and Discrete Mathematics
Type: Article
Journal: Journal of Geometry
Volume: 5
Pages: 85-94
No. of pages: 10
ISSN: 0047-2468
Publication date: 03.1974
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Geometry and Topology
Electronic version(s): https://doi.org/10.1007/BF01954538 (Access: Closed)