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Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings

Deng Yin Wang; Xian Wang — 2008

Archivum Mathematicum

Let $R$ be an arbitrary commutative ring with identity, $gl (n, R)$ the general linear Lie algebra over $R$ , $d (n, R)$ the diagonal subalgebra of $gl (n, R)$ . In case 2 is a unit of $R$ , all subalgebras of $gl (n, R)$ containing $d (n, R)$ are determined and their derivations are given. In case 2 is not a unit partial results are given.

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