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Abstract: Gyrogroup theory [A.A. Ungar, Thomas precession: its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics, Found. Phys. 27 (1997), pp. 881-951] enables the study of the algebra of Einstein's addition to be guided by analogies shared with the algebra of vector addition. The capability of gyrogroup theory to capture analogies is demonstrated in this article by exposing the Relativistic Composite-Velocity Reciprocity Principle. The breakdown of commutativity in ... (Update)
Context of citations to this paper: More
...= U , and in Fig. 4 for = C . The theory of gyrogroups and gyrovector spaces and its applications are presented in [1] 2] [3], and in a forthcoming book [4] where the advantages offered by the use of gyrogroup theoretic techniques in the manipulation of the...
Cited by: More
From the Group SL(2, C) to Gyrogroups and Gyrovector Spaces and .. - Chen, Ungar (Correct)
Active bibliography (related documents): More All
1.1: Decomposition of Groups into Twisted Subgroups and Subgroups - Tuval Foguel (Correct)
0.9: Involutory Decomposition of Groups Into Twisted Subgroups and.. - Foguel, Ungar (Correct)
0.6: From Pythagoras To Einstein: The Hyperbolic Pythagorean Theorem - Ungar (1998) (Correct)
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BibTeX entry: (Update)
A. A. Ungar, "The relativistic composite-velocity reciprocity principle," Found. Phys., vol. 30, no. 2, pp. 331--342, 2000. http://citeseer.ist.psu.edu/ungar00relativistic.html More
@misc{ ungar00relativistic,
author = "A. Ungar",
title = "The relativistic composite-velocity reciprocity principle",
text = "A. A. Ungar, The relativistic composite-velocity reciprocity principle,
Found. Phys., vol. 30, no. 2, pp. 331--342, 2000.",
year = "2000",
url = "citeseer.ist.psu.edu/ungar00relativistic.html" }
Citations (may not include all citations):9 An introduction to the theory of groups (context) - Rotman - 1995
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 Involutory decomposition of groups into twisted subgroups an.. - Foguel, Ungar - 2000
2 The abstract Lorentz transformation group (context) - Ungar - 1992
1 Gyrogroups and the decomposition of groups into twisted subg.. (context) - Foguel, Ungar - 2000
1 Translated from the German by G (context) - Pauli, relativity et al. - 1958
1 The Theory of Relativity (context) - Silberstein - 1914
1 The relativistic velocity composition paradox and the Thomas.. (context) - Ungar - 1989
1 Gyrovector spaces in the service of hyperbolic geometry (context) - Ungar - 1999
1 Reciprocity principle and the Lorentz tranformations (context) - Berzi, Gorini - 1969
1 ahlfors' rotation and gyrogroups (context) - Ungar, transformations et al. - 2000
1 A note on the Lorentz transformations linking initial and fi.. (context) - Ungar - 1992
1 Beitr age zur nichteuklidischen geometrie [contributions to .. (context) - cak - 1908
1 Uber die nichteuklidische interpretation der relativit atsth.. (context) - cak - 1912
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)
Involutory Decomposition of Groups Into Twisted Subgroups and.. - Foguel, Ungar (Correct)
From the Group SL(2, C) to Gyrogroups and Gyrovector Spaces and .. - Chen, Ungar (Correct)
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