On behavior of solvable ideals of Lie algebras under outer derivations
| dc.creator | Petravchuk, Anatoliy P. | |
| dc.date | 2008-08-24 | |
| dc.date.accessioned | 2026-07-07T09:58:12Z | |
| dc.date.available | 2026-07-07T09:58:12Z | |
| dc.description | Let $L$ be a finite dimensional Lie algebra over a field $F$. It is well known that the solvable radical $S(L)$ of the algebra $L$ is a characteristic ideal of $L$ if $\char F=0$ and there are counterexamples to this statement in case $\char F=p>0$. We prove that the sum $S(L)$ of all solvable ideals of a Lie algebra $L$ (not necessarily finite dimensional) is a characteristic ideal of $L$ in the following cases: 1) $\char F=0;$ 2) $S(L)$ is solvable and its derived length is less than $\log_{2}p.$ Some estimations (in characteristic 0) for the derived length of ideals $I+D(I)+... +D^{k}(I)$ are obtained where $I$ is a solvable ideal of $L$ and $D\in Der(L).$ | |
| dc.identifier | https://arxiv.org/abs/0808.3262 | |
| dc.identifier | http://arxiv.org/abs/0808.3262 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167629 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17B40; 17B30 | |
| dc.title | On behavior of solvable ideals of Lie algebras under outer derivations | |
| dc.type | text |