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Abstract: this paper is to present a natural way in which the algebra of the SL(2; C) group leads to gyrogroups and gyrovector spaces. This natural way convincingly demonstrates that the theory of gyrogroups and gyrovector spaces provides a most powerful formalism for dealing with the Lorentz group and hyperbolic geometry, the geometry that governs the special theory of relativity as well as other areas of physics (see, for instance, [9] and [10]). It is therefore hoped that, following this article,... (Update)
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BibTeX entry: (Update)
@misc{ chen-from,
author = "Jingling Chen and Abraham A. Ungar",
title = "From the Group SL(2, C) to Gyrogroups and Gyrovector Spaces and Huperbolic
Geometry",
url = "citeseer.ist.psu.edu/448396.html" }
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19 Quasigroups and loops: theory and applications (context) - Chein, Pflugfelder et al. - 1990
6 Thomas precession: its underlying gyrogroup axioms and their.. (context) - Ungar - 1997
5 From Pythagoras to Einstein: the hyperbolic Pythagorean theo.. - Ungar - 1998
4 Thomas rotation and the parametrization of the Lorentz trans.. (context) - Ungar - 1988
3 The hyperbolic Pythagorean theorem in the Poincar e disc mod.. (context) - Ungar - 1999
2 Physical holonomy, Thomas precession, and Clifford algebra (context) - Urbantke - 1990
2 K-loops, gyrogroups and symmetric spaces (context) - Krammer, Urbantke - 1998
2 A simple optical demonstration of geometric phases from mult.. (context) - on, anchez-Soto - 2001
2 Hyperbolic trigonometry in the Einstein relativistic velocit.. (context) - Ungar - 2000
1 The bifurcation approach to hyperbolic geometry (context) - Ungar - 2000
1 The relativistic composite-velocity reciprocity principle - Ungar - 2000
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1 Momentum and spin of a particle with spin unity (context) - van Wyk - 1999
1 the Wigner angle and its relation with the defect of a trian.. (context) - Chen, Ge - 1998
1 Dordrecht: Kluwer Academic Publishers (context) - Sabinin, quasigroups - 1999
1 the notion of gyrogroup (context) - Sabinin, Sabinina et al. - 1998
1 A possible hidden symmetry and geometrical source of the pha.. (context) - Chen, Ge et al. - 1999
1 Prentice-Hall Inc (context) - Halpern, relativity et al. - 1968
1 Placing the Einstein addition centrally in special relativit.. (context) - Ungar - 2001
1 Gyrogroups and homogeneous loops (context) - Issa - 1999
1 The hyperbolic derivative in the poincar e ball model of hyp.. (context) - Birman, Ungar - 2001
1 On central extensions of gyrocommutative gyrogroups (context) - ozga - 2000
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Documents on the same site (http://hypatia.math.ndsu.nodak.edu/faculty/ungar/publications.html): More
Decomposition of Groups into Twisted Subgroups and Subgroups - Tuval Foguel (Correct)
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The Relativistic Composite-Velocity Reciprocity Principle - Ungar (2000) (Correct)
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