Geodesic
Phenomenologically symmetrical local Lie groups of transformations of the space~$R^s$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2009), pp. 10-21.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we define a phenomenologically symmetric local Lie group of transformations of an arbitrary-dimensional space. We take as a basis the axiom scheme of the theory of physical structures. Phenomenologically symmetric groups of transformations are nondegenerate both with respect to coordinates and to parameters. We obtain a multipoint invariant of this group of transformations and relate it with Ward quasigroups. We define a substructure of a physical structure as a certain phenomenologically symmetric subgroup of transformations. We establish a criterion for the phenomenological symmetry of the Lie group of transformations and prove the uniqueness of a structure with the minimal rank. We also introduce the notion of a phenomenologically symmetric product of physical structures.
Keywords: physical structure, phenomenologically symmetric Lie group of transformations. 
@article{IVM_2009_7_a1,
     author = {V. A. Kyrov},
     title = {Phenomenologically symmetrical local {Lie} groups of transformations of the space~$R^s$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {10--21},
     publisher = {mathdoc},
     number = {7},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_7_a1/}
}
TY  - JOUR
AU  - V. A. Kyrov
TI  - Phenomenologically symmetrical local Lie groups of transformations of the space~$R^s$
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 10
EP  - 21
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_7_a1/
LA  - ru
ID  - IVM_2009_7_a1
ER  - 
%0 Journal Article
%A V. A. Kyrov
%T Phenomenologically symmetrical local Lie groups of transformations of the space~$R^s$
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 10-21
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2009_7_a1/
%G ru
%F IVM_2009_7_a1
V. A. Kyrov. Phenomenologically symmetrical local Lie groups of transformations of the space~$R^s$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2009), pp. 10-21. http://geodesic.mathdoc.fr/item/IVM_2009_7_a1/

[1] Mikhailichenko G. G., Gruppovaya simmetriya fizicheskikh struktur, Barnaul–Gorno-Altaisk, 2003, 204 pp.

[2] Simonov A. A., “Obobschennoe matrichnoe umnozhenie kak ekvivalentnoe predstavlenie teorii fizicheskikh struktur”, Prilozh. k knige Kulakova Yu. I., Teoriya fizicheskikh struktur, OOO “Kompaniya Yunivers Kontrakt”, M., 2004, 675–707

[3] Mikhailichenko G. G., “Fenomenologicheskaya i gruppovaya simmetriya v geometrii dvukh mnozhestv (teorii fizicheskikh struktur)”, DAN SSSR, 28:1 (1985), 39–41 | MR

[4] Akivis M. A., Shelekhov A. M., Vvedenie v teoriyu tri-tkanei, KGU, Kalinin, 1985, 84 pp.

[5] Mikhailichenko G. G., “Dvumetricheskie fizicheskie struktury ranga $(n+1,2)$”, Sib. matem. zhurn., 34:3 (1993), 132–143 | MR | Zbl

[6] Belousov V. D., Osnovy teorii kvazigrupp i lup, Nauka, M., 1967, 224 pp. | MR | Zbl

[7] Pontryagin L. S., Nepreryvnye gruppy, Nauka, M., 1973, 527 pp. | MR | Zbl

[8] Chatterjea S. K., “On Ward quasigroups”, Pure Math. Manuscript., 6 (1987), 31–34 | MR | Zbl

[9] Mikhailichenko G. G., Polimetricheskie geometrii, NGU, Novosibirsk, 2001, 146 pp.

[10] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978, 399 pp. | MR | Zbl