SCAP-subalgebras of Lie algebras

Chehrazi, Sara; Salemkar, Ali Reza

doi:10.1007/s10587-016-0317-3

Geodesic

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SCAP-subalgebras of Lie algebras

Chehrazi, Sara ; Salemkar, Ali Reza

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 4, pp. 1177-1184.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Résumé

A subalgebra

H

of a finite dimensional Lie algebra

L

is said to be a

S C A P

-subalgebra if there is a chief series

0 = L_{0} \subset L_{1} \subset \dots \subset L_{t} = L

L

such that for every

i = 1, 2, \dots, t

, we have

H + L_{i} = H + L_{i - 1}

H \cap L_{i} = H \cap L_{i - 1}

. This is analogous to the concept of

S C A P

-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its

S C A P

-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable.

MR Zbl

DOI : 10.1007/s10587-016-0317-3

Classification : 17B05, 17B30, 17B50
Mots-clés : Lie algebra;

S C A P

-subalgebra; chief series; solvable; supersolvable

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     title = {SCAP-subalgebras of {Lie} algebras},
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Chehrazi, Sara; Salemkar, Ali Reza. SCAP-subalgebras of Lie algebras. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 4, pp. 1177-1184. doi : 10.1007/s10587-016-0317-3. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0317-3/

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