| Title:
|
Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings (English) |
| Author:
|
Wang, Dengyin |
| Author:
|
Wang, Xian |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
173-183 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be an arbitrary commutative ring with identity, $\operatorname{gl}(n,R)$ the general linear Lie algebra over $R$, $d(n,R)$ the diagonal subalgebra of $\operatorname{gl}(n,R)$. In case 2 is a unit of $R$, all subalgebras of $\operatorname{gl}(n,R)$ containing $d(n,R)$ are determined and their derivations are given. In case 2 is not a unit partial results are given. (English) |
| Keyword:
|
the general linear Lie algebra |
| Keyword:
|
derivations of Lie algebras |
| Keyword:
|
commutative rings |
| MSC:
|
13C10 |
| MSC:
|
17B40 |
| MSC:
|
17B45 |
| idZBL:
|
Zbl 1212.13003 |
| idMR:
|
MR2462972 |
| . |
| Date available:
|
2009-01-29T09:14:44Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119756 |
| . |
| Reference:
|
[1] Benkart, G. M., Osbom, J. M.: Derivations and automorphisms of non-associative matrix algebras.Trans. Amer. Math. Soc. 263 (1981), 411–430. MR 0594417, 10.1090/S0002-9947-1981-0594417-5 |
| Reference:
|
[2] Cao, Y., Tang, Z.: Automorphisms of the Lie algebras of strictly upper triangular matrices over a commutative ring.Linear Algebra Appl. 360 (2003), 105–122. MR 1948476 |
| Reference:
|
[3] Jøndrup, S.: Automorphisms of upper triangular matrix rings.Arch. Math. 49 (1987), 497–502. MR 0921115, 10.1007/BF01194296 |
| Reference:
|
[4] Jøndrup, S.: The group of automorphisms of certain subalgebras of matrix algebras.J. Algebra 141 (1991), 106–114. MR 1118318, 10.1016/0021-8693(91)90206-N |
| Reference:
|
[5] Jøndrup, S.: Automorphisms and derivations of upper triangular matrix rings.Linear Algebra Appl. 221 (1995), 205–218. MR 1331800 |
| Reference:
|
[6] Wang, D., Ou, S., Yu, Q.: Derivations of the intermediate Lie algebras between the Lie algebra of diagonal matrices and that of upper triangular matrices over a commutative ring.Linear and Multilinear Algebra 54 (2006), 369 – 377. Zbl 1161.17312, MR 2236037, 10.1080/03081080500412463 |
| Reference:
|
[7] Wang, D., Yu, Q.: Derivations of the parabolic subalgebras of the general linear Lie algebra over a commutative ring.Linear Algebra Appl. 418 (2006), 763–774. Zbl 1161.17313, MR 2260227 |
| . |
