| Title:
|
Some necessary and sufficient conditions for nilpotent $n$-Lie superalgebras (English) |
| Author:
|
Guan, Baoling |
| Author:
|
Chen, Liangyun |
| Author:
|
Ma, Yao |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
1019-1034 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper studies nilpotent $n$-Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel's theorem for $n$-Lie superalgebras which is a generalization of those for $n$-Lie algebras and Lie superalgebras. In addition, as an application of Engel's theorem, we give some properties of nilpotent $n$-Lie superalgebras and obtain several sufficient conditions for an $n$-Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal and the Jacobson radical. (English) |
| Keyword:
|
nilpotent $n$-Lie superalgebra |
| Keyword:
|
Engel's theorem |
| Keyword:
|
$S^{\ast }$ algebra |
| Keyword:
|
Frattini subalgebra |
| MSC:
|
17A42 |
| MSC:
|
17A70 |
| MSC:
|
17B45 |
| MSC:
|
17B50 |
| idZBL:
|
Zbl 06433711 |
| idMR:
|
MR3304795 |
| DOI:
|
10.1007/s10587-014-0150-5 |
| . |
| Date available:
|
2015-02-09T17:37:32Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144158 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
