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- Publications
- Influence
Recent developments on absolute geometries and algebraization by K-loops
- H. Karzel
- Computer Science, Mathematics
- Discret. Math.
- 1 October 1999
Let (P,L,α) be an ordered space. A spatial version of Pasch's assertion is proved, with that a short proof is given for the fact that (P,L) is an exchange space and the concepts h-parallel, one sided… Expand
Legendre-like Theorems in a General Absolute Geometry
Abstract.In this paper the axiomatic basis will be a general absolute plane A = (
$${\mathcal{P}}, {\mathcal{L}}, \alpha, \equiv$$
) in the sense of [6], where
$${\mathcal{P}}$$
and … Expand
A geometric construction of the K-loop of a hyperbolic space
- H. Karzel, H. Wefelscheid
- Mathematics
- 1 December 1995
It is well known that the homogeneous orthochronous proper Lorentzgroup Γ is isomorphic to the proper motion group of the hyperbolic space. To each Lorentz boost β ε Γ \ {id} there corresponds in the… Expand
Webs related to K-loops and reflection structures
- E. Gabrieli, Bokhee Im, H. Karzel
- Mathematics
- 1 December 1999
We give a characterization of webs (P,g1,g2,g) which are related to A1-loops, weakK-loops,K-loops and reflection structures. We also obtain a geometric proof of Kreuzer’S result that the concept… Expand
Groups With An Involutory Antiautomorphism And K-Loops; Application To Space-Time-World And Hyperbolic Geometry I
- H. Karzel, H. Wefelscheid
- Mathematics
- 1 May 1993
Reflection groups and K-loops
AbstractThe notion “reflection group” (Γ,
$$\mathcal{D}$$
) was introduced in order to give group theoretical characterizations of absolute planes. Here we consider “reflection groups with midpoints”… Expand
Webs with rotation and reflection properties and their relations with certain loops
In a web one can define in a natural way reflections in generators and a kind of rotations in points. The structure of the webs and the corresponding loops in which some of these maps are… Expand
Electronic topological transition in zinc metal at high external pressure
- M. Steiner, W. Potzel, +4 authors P. Blaha
- Chemistry
- 13 May 1996
We report investigations of Zn metal under quasi-hydrostatic pressures up to 16 GPa by Mossbauer spectroscopy and scalar - relativistic linearized augmented plane wave (LAPW) calculations. Our… Expand
The Reflection Structures of Generalized Co-Minkowski Spaces Leading to K-Loops
- E. Gabrieli, H. Karzel
- Mathematics
- 1 August 1997
We extend the notion co- Minkowski plane to “unitary co- Minkowski space” (P, G, ∼) and discuss the problem whether there are subsets Q of P which can be turned into a geometric K- loop.
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