Geodesic
Composition algebras of arbitrary degrees
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 16-21.

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In this paper, a generalization of composition algebras is given, in which the quadratic form is replaced by a form of arbitrary degree. Two series of generalized composition algebras are found: cyclic algebras of arbitrary order and algebras that are obtained by the generalized doubling procedure applied to cyclic algebras.
Mots-clés : composition algebra
Keywords: Hurwitz problem, cyclic algebra, doubling procedure. 
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N. I. Guseva; E. V. Lukyanova. Composition algebras of arbitrary degrees. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 16-21. http://geodesic.mathdoc.fr/item/INTO_2020_181_a2/

[1] Aleksandrova N. V., Iz istorii vektornogo ischisleniya, MAI, M., 1992

[2] Burlakov M. P., Gamiltonovy algebry, Graf-Press, M., 2006

[3] Guseva N. I., Burlakov I. M., Burlakov M. P., Elementarnaya geometriya v prostranstvakh nad algebrami, Intellekt-Tsentr, M., 2017

[4] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR

[5] Proskuryakov I. V., Sbornik zadach po lineinoi algebre, Nauka, M., 1967

[6] Khund F., Istoriya kvantovoi teorii, Naukova dumka, Kiev, 1980