Geodesic
Standard Envelopes of Commutative Triple Systems
Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 733-739.

Voir la notice de l'article provenant de la source Math-Net.Ru

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). 
@article{MZM_2001_69_5_a8,
     author = {V. T. Filippov},
     title = {Standard {Envelopes} of {Commutative} {Triple} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {733--739},
     publisher = {mathdoc},
     volume = {69},
     number = {5},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a8/}
}
TY  - JOUR
AU  - V. T. Filippov
TI  - Standard Envelopes of Commutative Triple Systems
JO  - Matematičeskie zametki
PY  - 2001
SP  - 733
EP  - 739
VL  - 69
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a8/
LA  - ru
ID  - MZM_2001_69_5_a8
ER  - 
%0 Journal Article
%A V. T. Filippov
%T Standard Envelopes of Commutative Triple Systems
%J Matematičeskie zametki
%D 2001
%P 733-739
%V 69
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a8/
%G ru
%F MZM_2001_69_5_a8
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