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International Journal of Theoretical Physics

, Volume 40, Issue 1, pp 359–362 | Cite as

Nonassociative Geometry of Special Relativity

  • Larissa Sbitneva
Article

Abstract

The nonassociative axiomatics of the relativistic law of composition of velocities in special relativity is presented. For the first time the canomical unary operations are considered.

Keywords

Field Theory Elementary Particle Quantum Field Theory Special Relativity Unary Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

  1. Fok, Vladimir A. (1955). The Theory of Space, Time and Gravitation, (in Russian) GITTL, Moscow. English translation, Pergamon Press (1959) MR21 #7042.Google Scholar
  2. Nesterov, Alexander I. (1989). The methods of nonassociative algebra in physics, Doctor of Sciences Dissertation, Institute of Physics of Estonian Academy of Sciences, Tartu.Google Scholar
  3. Sabinin, Lev V. (1981). Methods of nonassociative algebra in differential geometry, in: Shoshichi Kobayashi and Katsumi Nomizy, Foundations of Differential Geometry, [in Russian], Nauka, Moscow, Vol. 1, Supplement, pp. 293–339; MR 84b:53002.Google Scholar
  4. Sabinin, Lev V. (1991). Analytic Quasigroups and Geometry, Friendship of Nations University, Moscow.Google Scholar
  5. Sabinin, Lev V. (1995). On gyrogroups of Ungar, Advances in Mathematical Sciences, 50(5), 251–252 [in Russian]; English translation: Russian Mathematical Survey, 50(5).Google Scholar
  6. Sabinin, Lev V. (1999). Smooth Quasigroups and Loops, Kluwer, Dordrecht.Google Scholar
  7. Sabinin, Lev V., and P. O. Miheev (1993). On the law of addition of velocities in special relativity, Advances in Mathematical Sciences, 48(5), 183–184 [in Russian]. English translation: Russian Mathematical Survey, 48(5).Google Scholar
  8. Sabinin, Lev V., and Alexander I. Nesterov (1997). Smooth loops and Thomas precession, Hadronic Journal, 20, 219–237.Google Scholar
  9. Sabinin, Lev V., Ludmila L. Sabinina, and Larissa V. Sbitneva (1998). On the notion of gyrogroup, Aequationes Mathematicae, 56(1), 11–17.Google Scholar
  10. Sabinin, Lev V., and Larissa V. Sbitneva (1994). Half Bol loops, in: Webs and Quasigroups, Tver University Press, pp. 50–54.Google Scholar
  11. Ungar, Abraham A. (1990). Weakly associative groups, Results in Mathematics, 17, 149–168.Google Scholar
  12. Ungar, Abraham A. (1994). The holomorphic automorphism group of the complex disk, Aequationes Mathematicae, 17(2), 240–254.Google Scholar
  13. Ungar, Abraham A. (1997). Thomas precession: Its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics, Foundations of Physics, 27, 881–951.Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Larissa Sbitneva
    • 1
  1. 1.División de Cienicias e Ingeniería, Departmento de MatematicasUniversidad de Quintana RooChetumal, Ouintana RooMexico

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