Geodesic
Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings
Archivum mathematicum, Tome 44 (2008) no. 3, pp. 173-183.

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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.
Classification : 13C10, 17B40, 17B45
Keywords: the general linear Lie algebra; derivations of Lie algebras; commutative rings 
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     author = {Wang, Dengyin and Wang, Xian},
     title = {Derivations of the subalgebras intermediate the general linear {Lie} algebra and the diagonal subalgebra over commutative rings},
     journal = {Archivum mathematicum},
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     publisher = {mathdoc},
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     zbl = {1212.13003},
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Wang, Dengyin; Wang, Xian. Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings. Archivum mathematicum, Tome 44 (2008) no. 3, pp. 173-183. http://geodesic.mathdoc.fr/item/ARM_2008__44_3_a0/