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Keywords:
the general linear Lie algebra; derivations of Lie algebras; commutative rings
the general linear Lie algebra; derivations of Lie algebras; commutative rings
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.
References:
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