Non-associative geometry and discrete structure of spacetime

Alexander I. Nesterov; Lev Vasilʹevich Sabinin

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 2, page 347-357
  • ISSN: 0010-2628

Abstract

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A new mathematical theory, {\it non-associative geometry}, providing a unified algebraic description of continuous and discrete spacetime, is introduced.

How to cite

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Nesterov, Alexander I., and Sabinin, Lev Vasilʹevich. "Non-associative geometry and discrete structure of spacetime." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 347-357. <http://eudml.org/doc/248646>.

@article{Nesterov2000,
abstract = {A new mathematical theory, \{\it non-associative geometry\}, providing a unified algebraic description of continuous and discrete spacetime, is introduced.},
author = {Nesterov, Alexander I., Sabinin, Lev Vasilʹevich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {smooth loops; geomodular structure},
language = {eng},
number = {2},
pages = {347-357},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Non-associative geometry and discrete structure of spacetime},
url = {http://eudml.org/doc/248646},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Nesterov, Alexander I.
AU - Sabinin, Lev Vasilʹevich
TI - Non-associative geometry and discrete structure of spacetime
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 2
SP - 347
EP - 357
AB - A new mathematical theory, {\it non-associative geometry}, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
LA - eng
KW - smooth loops; geomodular structure
UR - http://eudml.org/doc/248646
ER -

References

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  2. Sabinin L.V., On the equivalence of categories of loops and homogeneous spaces, Soviet Math. Dokl. 13 (1972a), 970. (1972a) Zbl0291.18006
  3. Sabinin L.V., The geometry of loops, Mathematical Notes 12 799 (1972b). (1972b) MR0340461
  4. Sabinin L.V., Odules as a new approach to a geometry with a connection, Soviet Math. Dokl. 18 515 (1977). (1977) Zbl0375.53021
  5. Sabinin L.V., Methods of Nonassociative Algebra in Differential Geometry, in Supplement to Russian translation of S.K. Kobayashi and K. Nomizu ``Foundations of Differential Geometry'', Vol. 1., Moscow, Nauka, 1981. MR0628734
  6. Sabinin L.V., Differential equations of smooth loops, in: Proc. of Sem. on Vector and Tensor Analysis 23, Moscow Univ., Moscow, 1988, p.133. Zbl0829.53016MR1041276
  7. Sabinin L.V., Differential Geometry and Quasigroups, Proc. Inst. Math. Siberian Branch of Acad. Sci. USSR 14, 1989, p.208. Zbl0714.53016MR1040489
  8. Sabinin L.V., On differential equations of smooth loops, Russian Mathematical Survey 49 172 (1994). (1994) Zbl0829.53016MR1283149
  9. Sabinin L.V., Smooth quasigroups and loops, Kluwer Academic Publishers, Dordrecht, 1999. Zbl1038.20051MR1727714
  10. Eguchi T., Gilkey P.B., Hanson A.J., Gravitation, Gauge theory and differential geometry, journal ??? 66 213-393 (1980). (1980) MR0598586
  11. Nesterov A.I., Stepanenko V.A., On methods of non-associative algebra in geometry and physics, preprint No400 F, Institute of Physics, Krasnoyarsk, Russia, 1986. 
  12. Nesterov A.I., Sabinin L.V., Smooth loops and Thomas Precession, Hadronic J. 20 (1997), 219-237. (1997) Zbl0936.20056MR1676951
  13. Nesterov A.I., Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity, Phys. Rev. D 56, R7498 - R7502 (1997). MR1603654

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