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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 sidedExpand
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Development of non-Euclidean geometries since Gauß
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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
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A geometric construction of the K-loop of a hyperbolic space
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 theExpand
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Webs related to K-loops and reflection structures
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 conceptExpand
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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
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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 areExpand
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Electronic topological transition in zinc metal at high external pressure
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. OurExpand
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The Reflection Structures of Generalized Co-Minkowski Spaces Leading to K-Loops
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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