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. 
@article{AL_2002_41_1_a2,
     author = {A. T. Gainov},
     title = {$Z_n${-Orthograded} {Monocomposition} {Algebras}},
     journal = {Algebra i logika},
     pages = {57--69},
     publisher = {mathdoc},
     volume = {41},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_1_a2/}
}
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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/