On Right Symmetric and Novikov Nil-Algebras of Bounded Index
Matematičeskie zametki, Tome 70 (2001) no. 2, pp. 289-295
Cet article a éte moissonné depuis la source Math-Net.Ru
Let $\Phi$ be a field of characteristic zero. It is proved that a right symmetric nil-algebra of index $n$ over $\Phi$ is right nilpotent, and a Novikov nil-algebra of index $n$ over $\Phi$ is nilpotent.
@article{MZM_2001_70_2_a11,
author = {V. T. Filippov},
title = {On {Right} {Symmetric} and {Novikov} {Nil-Algebras} of {Bounded} {Index}},
journal = {Matemati\v{c}eskie zametki},
pages = {289--295},
year = {2001},
volume = {70},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_2_a11/}
}
V. T. Filippov. On Right Symmetric and Novikov Nil-Algebras of Bounded Index. Matematičeskie zametki, Tome 70 (2001) no. 2, pp. 289-295. http://geodesic.mathdoc.fr/item/MZM_2001_70_2_a11/
[1] Balinskii A. A., Novikov S. P., “Skobki Puassona gidrodinamicheskogo tipa, frobeniusovy algebry i algebry Li”, Dokl. AN SSSR, 283:5 (1985), 1036–1039 | MR | Zbl
[2] Osborn J. M., “Novikov algebras”, Nova J. Algebra Geometry, 1:1 (1992), 1–13 | MR | Zbl
[3] Vinberg E. B., “Vypuklye odnorodnye oblasti”, Dokl. AN SSSR, 141:3 (1961), 521–524 | MR | Zbl
[4] Zelmanov E. I., “Ob engelevykh algebrakh Li”, Sib. matem. zh., 29:5 (1988), 112–117 | MR | Zbl
[5] Zelmanov E. I., “Ob odnom klasse lokalnykh translyatsionno invariantnykh algebr Li”, Dokl. AN SSSR, 292:6 (1987), 1294–1297 | MR | Zbl