Projective geometry and phenomenological symmetry
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 1, pp. 82-90.

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In this paper it is investigated the physical structure of the maximal range in a projective space $(PV)^s$ over the algebra of hypercomplex numbers $V$. It is proved that this structure is formed by the group of projective transforms of the space $(PV)^s$.
Keywords: projective space, group of projective transforms.
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Vladimir A. Kyrov. Projective geometry and phenomenological symmetry. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 1, pp. 82-90. http://geodesic.mathdoc.fr/item/JSFU_2012_5_1_a8/

[1] N. V. Efimov, Vysshaya geometriya, FM, M., 1961 | MR

[2] A. A. Simonov, “Obobschennoe matrichnoe umnozhenie kak ekvivalentnoe predstavlenie teorii fizicheskikh struktur”, Prilozhenie k knige: Kulakov Yu. I., Teoriya fizicheskikh struktur, Kompaniya Yunivers Kontrakt, M., 2004

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

[4] L. S. Pontryagin, Nepreryvnye gruppy, Nauka, M., 1973 | MR | Zbl

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

[6] G. G. Mikhailichenko, R. M. Muradov, Fizicheskie struktury kak geometrii dvukh mnozhestv, Izd-vo Gorno-Alt. gos. un-ta, Gorno-Altaisk, 2008

[7] E. B. Vinberg, A. L. Onischik, “Osnovy teorii grupp Li”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 20, VINITI, M., 1988, 5–101 | MR | Zbl

[8] G. G. Mikhailichenko, “Fenomenologicheskaya i gruppovaya simmetriya v geometrii dvukh mnozhestv (teorii fizicheskikh struktur)”, Dokl. AN SSSR, 24:1 (1985), 39–41 | MR

[9] V. V. Gorbatsevich, A. L. Onischik, “Gruppy Li preobrazovanii”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 20, VINITI, M., 1988, 103–240 | MR | Zbl