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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

36 1

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

2 1

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

22 1

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

11 1

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

34 1

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

17 1

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

2 1

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

13

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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