Geodesic
$\mathbb Z_3$-orthograded quasimonocomposition algebras with one-dimensional null component
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 141-144 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider $\mathbb Z_3$-orthograded nondegenerate quasimonocomposition algebras $A=A_0\oplus A_1\oplus A_2$ such that $\dim A_0=1$ and $A_1A_2=0$. It is proved that all algebras in this class $W$ are solvable of solvability index either two or three. All non bi-isotropic orthogonal nonisomorphic algebras $A$ of $W$ of least dimension, which is equal to $9$, are classified. An infinite series of algebras $C_r$ in $W$ of dimension $\dim C_r=8r+1$ is constructed for every $r\in\mathbb N=\{1,2,\dots\}$. All algebras $C_r$ are solvable of solvability index $3$ and nilpotent of nil-index $5$. 
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     title = {$\mathbb Z_3$-orthograded quasimonocomposition algebras with one-dimensional null component},
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     pages = {141--144},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2005_2_a22/}
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A. T. Gainov. $\mathbb Z_3$-orthograded quasimonocomposition algebras with one-dimensional null component. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 141-144. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a22/

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