Geodesic
$Z_n$-Orthograded Monocomposition Algebras
Algebra i logika, Tome 41 (2002) no. 1, pp. 57-69.

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We study NQM algebras $A$ having an orthogonal automorphism $\varphi$ of finite order $n\geqslant3 $ (called $Z_n$-orthograded NQM algebras). The $Z_3$-orthograded NQM algebras of dimension 7 are treated in more detail. In particular, we find all algebras $A$ which are not bi-isotropic in this class, and for every algebra $A$, determine an automorphism group $\operatorname{Aut}A$ and an orthogonal automorphism group $\operatorname{Ortaut}A$. In constructing and classifying (up to isomorphism) NQM algebras, use is made of orthogonal decompositions of the algebras.
Keywords: $Z_n$-orthograded $\rm NQM$ algebra
Mots-clés : orthogonal decomposition of algebras, automorphism group, orthogonal automorphism group. 
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A. T. Gainov. $Z_n$-Orthograded Monocomposition Algebras. Algebra i logika, Tome 41 (2002) no. 1, pp. 57-69. http://geodesic.mathdoc.fr/item/AL_2002_41_1_a2/

[1] A. T. Gainov, “Izomorfizmy konechnomernykh nevyrozhdennykh monokompozitsionnykh algebr”, Matem. zametki, 25:6 (1979), 801–810 | MR

[2] A. T. Gainov, “Simmetricheskie podalgebry monokompozitsionnykh algebr”, Algebra i logika, 27:5 (1988), 503–526 | MR | Zbl

[3] K. Atsuyama, “Symmetric spaces derived from algebras”, Kodai Math. J., 3 (1980), 358–363 | DOI | MR | Zbl

[4] A. T. Gainov, “Tsvetnye monokompozitsionnye algebry”, Kurosh algebraic conference 98, Abstracts of talks, M., 1998, 157–158

[5] N. Dzhekobson, Algebry Li, Mir, M., 1964 | MR

[6] A. T. Gainov, “Monokompozitsionnye algebry s biizotropnoi KM-algebroi”, Matem. issled., VII:3(25) (1972), 41–68, Kishinev | MR

[7] P. I. Vasilev, “Minimalnaya razmernost nebiizotropnykh KM-algebr”, Sib. matem. zh., 14:5 (1973), 927–932 | MR