Geodesic
Simple right-alternative unital superalgebras over an algebra of matrices of order~$2$
Algebra i logika, Tome 58 (2019) no. 1, pp. 108-131.

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We classify simple right-alternative unital superalgebras over a field of characteristic not $2$, whose even part coincides with an algebra of matrices of order $2$. It is proved that such a superalgebra either is a Wall double $W_{2|2}(\omega)$, or is a Shestakov super algebra $S_{4|2}(\sigma)$ (characteristic $3$), or is isomorphic to an asymmetric double, an $8$-dimensional superalgebra depending on four parameters. In the case of an algebraically closed base field, every such superalgebra is isomorphic to an associative Wall double $\mathrm{M}_2[\sqrt{1}]$, an alternative $6$-dimensional Shestakov superalgebra $B_{4|2}$ (characteristic $3$), or an $8$-dimensional Silva–Murakami–Shestakov superalgebra.
Keywords: right-alternative superalgebra, simple superalgebra. 
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S. V. Pchelintsev; O. V. Shashkov. Simple right-alternative unital superalgebras over an algebra of matrices of order~$2$. Algebra i logika, Tome 58 (2019) no. 1, pp. 108-131. http://geodesic.mathdoc.fr/item/AL_2019_58_1_a6/

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