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
Access Full Article
topAbstract
topHow to cite
topNesterov, 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, 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 = {quasigroups; smooth loops; spacetime; 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, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
LA - eng
KW - quasigroups; smooth loops; spacetime; smooth loops; geomodular structure
UR - http://eudml.org/doc/248646
ER -
References
top- Kikkawa M., On local loops in affine manifolds, J. Sci. Hiroshima Univ. Ser A-I Math. 28 (1961), 199. (1961) MR0187173
- Sabinin L.V., On the equivalence of categories of loops and homogeneous spaces, Soviet Math. Dokl. 13 (1972a), 970. (1972a) Zbl0291.18006
- Sabinin L.V., The geometry of loops, Mathematical Notes 12 799 (1972b). (1972b) MR0340461
- Sabinin L.V., Odules as a new approach to a geometry with a connection, Soviet Math. Dokl. 18 515 (1977). (1977) Zbl0375.53021
- 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
- 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
- Sabinin L.V., Differential Geometry and Quasigroups, Proc. Inst. Math. Siberian Branch of Acad. Sci. USSR 14, 1989, p.208. Zbl0714.53016MR1040489
- Sabinin L.V., On differential equations of smooth loops, Russian Mathematical Survey 49 172 (1994). (1994) Zbl0829.53016MR1283149
- Sabinin L.V., Smooth quasigroups and loops, Kluwer Academic Publishers, Dordrecht, 1999. Zbl1038.20051MR1727714
- Eguchi T., Gilkey P.B., Hanson A.J., Gravitation, Gauge theory and differential geometry, journal ??? 66 213-393 (1980). (1980) MR0598586
- 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.
- Nesterov A.I., Sabinin L.V., Smooth loops and Thomas Precession, Hadronic J. 20 (1997), 219-237. (1997) Zbl0936.20056MR1676951
- Nesterov A.I., Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity, Phys. Rev. D 56, R7498 - R7502 (1997). MR1603654
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.