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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     author = {N. I. Guseva and E. V. Lukyanova},
     title = {Composition algebras of arbitrary degrees},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {16--21},
     publisher = {mathdoc},
     volume = {181},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_181_a2/}
}
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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/