| Title:
|
SCAP-subalgebras of Lie algebras (English) |
| Author:
|
Chehrazi, Sara |
| Author:
|
Salemkar, Ali Reza |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
1177-1184 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subalgebra $H$ of a finite dimensional Lie algebra $L$ is said to be a $\rm SCAP$-subalgebra if there is a chief series $0=L_0\subset L_1\subset \ldots \subset L_t=L$ of $L$ such that for every $i=1,2,\ldots ,t$, we have $H+L_i=H+L_{i-1}$ or $H\cap L_i=H\cap L_{i-1}$. This is analogous to the concept of $\rm SCAP$-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 $\rm SCAP$-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable. (English) |
| Keyword:
|
Lie algebra |
| Keyword:
|
$\rm SCAP$-subalgebra |
| Keyword:
|
chief series |
| Keyword:
|
solvable |
| Keyword:
|
supersolvable |
| MSC:
|
17B05 |
| MSC:
|
17B30 |
| MSC:
|
17B50 |
| idZBL:
|
Zbl 06674869 |
| idMR:
|
MR3572930 |
| DOI:
|
10.1007/s10587-016-0317-3 |
| . |
| Date available:
|
2016-11-26T20:58:47Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145926 |
| . |
| Reference:
|
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