Affine Geometry as a~Physical Structure
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 4, pp. 460-464.

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We consider the physical structure of maximal rank in the affine space $V^s$ over the algebra of hypercomplex numbers $V$. It is proved that this structure is given by the group of affine transformations of the space $V^s$.
Keywords: physical structure, hypercomplex numbers.
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Vladimir A. Kyrov. Affine Geometry as a~Physical Structure. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 4, pp. 460-464. http://geodesic.mathdoc.fr/item/JSFU_2008_1_4_a10/

[1] I. L. Kantor, A. S. Solodovnikov, Giperkompleksnye chisla, Nauka, M., 1973 | MR

[2] R. M. Muradov, “Giperkompleksnye chisla ranga 3”, Nauka. Kultura. Obrazovanie. Gorno-Altaisk, 2004, no. 15/16, 107

[3] V. A. Kyrov, “Kvazigruppovye svoistva affinnykh grupp”, Doklady VI Sibirskoi nauchnoi shkoly-seminara s mezhdunarodnym uchastiem “Kompyuternaya bezopasnost i kriptografiya – SIBECRYPT' 07”, Prilozhenie k zhurnalu Vestnik Tomskogo gosudarstvennogo universiteta. Seriya Matematika, Kibernetika, Informatika, 2007, no. 23, 37–41

[4] A. A. Simonov, “Obobschennoe matrichnoe umnozhenie kak ekvivalentnoe predstavlenie teorii fizicheskikh struktur”, Prilozhenie k knige Kulakova Yu. I., Teoriya fizicheskikh struktur, M., 2004

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

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

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

[8] N. V. Efimov, Vysshaya geometriya, Fizmatgiz, M., 1961 | MR