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VOL. 15 | 2014 Vector Parameters in Classical Hyperbolic Geometry
Danail S. Brezov, Clementina D. Mladenova, Ivaïlo M. Mladenov

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

Abstract

Here we use an extension of Rodrigues' vector parameter construction for pseudo-rotations in order to obtain explicit formulae for the generalized Euler decomposition with arbitrary axes for the structure groups in the classical models of hyperbolic geometry. Although the construction is projected from the universal cover $\,\mathsf{SU}(1,1)\simeq\mathsf{SL}(2,\mathbb{R})$, most attention is paid to the 2+1 Minkowski space model, following the close analogy with the Euclidean case, and various decompositions of the restricted Lorentz group $\mathsf{SO}^+(2,1)$ are investigated in detail. At the end we propose some possible applications in special relativity and scattering theory.

Information

Published: 1 January 2014
First available in Project Euclid: 13 July 2015

zbMATH: 1369.51005
MathSciNet: MR3287750

Digital Object Identifier: 10.7546/giq-15-2014-79-105

Rights: Copyright © 2014 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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