Geodesic
Reduced Lie ternary algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 508-516

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We introduce a notion of variety of RLT-algebras as a variety of ternary anticommutative algebras such that the Jacobian $J(x,y,z;u,v)$ (see (3)) is skew-symmetric in all the arguments. The algebras in this variety possess the property that their reduced algebra is a Lie algebra. We show that this variety properly contains the variety of Filippov algebras and coincides with the variety of Filippov algebras in the presence of a non-degenerate (skew)symmetric anti-invariant form. We also obtain some structure results on RLT-algebras.
Keywords: RLT-algebra, Filippov algebra, Engel theorem
Mots-clés : multiplication algebra. 
@article{SEMR_2014_11_a15,
     author = {A. P. Pozhidaev},
     title = {Reduced {Lie} ternary algebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {508--516},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a15/}
}
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A. P. Pozhidaev. Reduced Lie ternary algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 508-516. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a15/