Geodesic
Standard Envelopes of Commutative Triple Systems
Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 733-739 Cet article a éte moissonné depuis la source Math-Net.Ru

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Under certain constraints on the characteristic of a field $\Phi$, the commutative standard enveloping $q$-algebra $B$ of a commutative triple system $A$ over $\Phi$ is defined. It is proved that 1) if the algebra $B$ is simple, then the system $A$ is simple; 2) if the system $A$ is simple, then $B$ either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals). 
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V. T. Filippov. Standard Envelopes of Commutative Triple Systems. Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 733-739. http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a8/

[1] Filippov V. T., “Obertyvayuschie troinykh sistem i algebr”, Algebra i logika, 29:1 (1990), 67–81 | MR | Zbl

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

[3] Lister W. G., “A structure theory of Lie triple systems”, Trans. Amer. Math. Soc., 72:2 (1952), 217–242 | DOI | MR | Zbl