Details
| Original language | German |
|---|---|
| Pages (from-to) | 85-94 |
| Number of pages | 10 |
| Journal | Journal of Geometry |
| Volume | 5 |
| Issue number | 1 |
| Publication status | Published - Mar 1974 |
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.
ASJC Scopus subject areas
- Mathematics(all)
- Geometry and Topology
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In: Journal of Geometry, Vol. 5, No. 1, 03.1974, p. 85-94.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Einbettung gewisser Kettengeometrien in projektive Räume
AU - Hotje, Herbert
PY - 1974/3
Y1 - 1974/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=25444447882&partnerID=8YFLogxK
U2 - 10.1007/BF01954538
DO - 10.1007/BF01954538
M3 - Artikel
AN - SCOPUS:25444447882
VL - 5
SP - 85
EP - 94
JO - Journal of Geometry
JF - Journal of Geometry
SN - 0047-2468
IS - 1
ER -