Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings
Wang, Deng Yin ; Wang, Xian
Archivum Mathematicum, Tome 044 (2008), p. 173-183 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2008-01-01
Classification:  13C10,  17B40,  17B45 
@article{119756,
     author = {Deng Yin Wang and Xian Wang},
     title = {Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings},
     journal = {Archivum Mathematicum},
     volume = {044},
     year = {2008},
     pages = {173-183},
     zbl = {1212.13003},
     mrnumber = {2462972},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119756}
}

Wang, Deng Yin; Wang, Xian. Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings. Archivum Mathematicum, Tome 044 (2008) pp. 173-183. http://gdmltest.u-ga.fr/item/119756/

Benkart, G. M.; Osbom, J. M. Derivations and automorphisms of non-associative matrix algebras, Trans. Amer. Math. Soc. 263 (1981), 411–430. (1981) | Article | MR 0594417

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. (2003) | MR 1948476

Jøndrup, S. Automorphisms of upper triangular matrix rings, Arch. Math. 49 (1987), 497–502. (1987) | Article | MR 0921115

Jøndrup, S. The group of automorphisms of certain subalgebras of matrix algebras, J. Algebra 141 (1991), 106–114. (1991) | Article | MR 1118318

Jøndrup, S. Automorphisms and derivations of upper triangular matrix rings, Linear Algebra Appl. 221 (1995), 205–218. (1995) | MR 1331800

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. (2006) | Article | MR 2236037 | Zbl 1161.17312

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. (2006) | MR 2260227 | Zbl 1161.17313