| Title:
|
Non-associative geometry and discrete structure of spacetime (English) |
| Author:
|
Nesterov, Alexander I. |
| Author:
|
Sabinin, Lev V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
347-357 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A new mathematical theory, {\it non-associative geometry}, providing a unified algebraic description of continuous and discrete spacetime, is introduced. (English) |
| Keyword:
|
quasigroups |
| Keyword:
|
smooth loops |
| Keyword:
|
spacetime |
| MSC:
|
20N05 |
| MSC:
|
53B15 |
| MSC:
|
53C15 |
| MSC:
|
55R65 |
| MSC:
|
81T13 |
| MSC:
|
83A05 |
| idZBL:
|
Zbl 1036.53010 |
| idMR:
|
MR1780876 |
| . |
| Date available:
|
2009-01-08T19:01:54Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119168 |
| . |
| Reference:
|
[1] Kikkawa M.: On local loops in affine manifolds.J. Sci. Hiroshima Univ. Ser A-I Math. 28 (1961), 199. MR 0187173 |
| Reference:
|
[2] Sabinin L.V.: On the equivalence of categories of loops and homogeneous spaces.Soviet Math. Dokl. 13 (1972a), 970. Zbl 0291.18006 |
| Reference:
|
[3] Sabinin L.V.: The geometry of loops.Mathematical Notes 12 799 (1972b). MR 0340461 |
| Reference:
|
[4] Sabinin L.V.: Odules as a new approach to a geometry with a connection.Soviet Math. Dokl. 18 515 (1977). Zbl 0375.53021 |
| Reference:
|
[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. MR 0628734 |
| Reference:
|
[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. Zbl 0829.53016, MR 1041276 |
| Reference:
|
[7] Sabinin L.V.: Differential Geometry and Quasigroups.Proc. Inst. Math. Siberian Branch of Acad. Sci. USSR 14, 1989, p.208. Zbl 0714.53016, MR 1040489 |
| Reference:
|
[8] Sabinin L.V.: On differential equations of smooth loops.Russian Mathematical Survey 49 172 (1994). Zbl 0829.53016, MR 1283149 |
| Reference:
|
[9] Sabinin L.V.: Smooth quasigroups and loops.Kluwer Academic Publishers, Dordrecht, 1999. Zbl 1038.20051, MR 1727714 |
| Reference:
|
[10] Eguchi T., Gilkey P.B., Hanson A.J.: Gravitation, Gauge theory and differential geometry.journal ??? 66 213-393 (1980). MR 0598586 |
| Reference:
|
[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. |
| Reference:
|
[12] Nesterov A.I., Sabinin L.V.: Smooth loops and Thomas Precession.Hadronic J. 20 (1997), 219-237. Zbl 0936.20056, MR 1676951 |
| Reference:
|
[13] Nesterov A.I.: Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity.Phys. Rev. D 56, R7498 - R7502 (1997). MR 1603654 |
| . |
