Geodesic
On a generalization of the quaternion algebra
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 Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 1, Tome 220 (2023), pp. 33-37
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In this paper, we consider a generalization of quaternion algebras and hypercomplex Clifford algebras over the field of complex numbers in which the $m$th power of a vector of the underlying space is the sum of the $m$th powers of the coordinates of this vector.
Mots-clés : quaternions, group algebras
Keywords: Clifford algebras, cyclic algebras, doubling procedure. 
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I. M. Burlakov. On a generalization of the quaternion algebra. 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 Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 1, Tome 220 (2023), pp. 33-37. http://geodesic.mathdoc.fr/item/INTO_2023_220_a3/

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

[2] Burlakov I. M., Burlakov M. P., Geometricheskie struktury lineinykh algebr, LAMBERT, 2019

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

[4] Burlakov M. P., Burlakov I. M., Guseva N. I., Ocherki ob algebrakh tsiklicheskikh chisel, Izd-vo «Kim», M., 2020

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

[6] Mikesh I., Burlakov M. P., Yukl M., Burlakov I. M., Giperkompleksnye struktury vysshikh poryadkov, Izd-vo «Kim», M.–Olomouts, 2020

[7] Delanghe R., Bracks F., Sommen F., Clifford Analysis, Pitnam Publ., Boston–London–Melbourne, 1982