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Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings. (English) Zbl 1212.13003
Summary: Let $$R$$ be an arbitrary commutative ring with identity, $$\text{gl} (n,R)$$ the general linear Lie algebra over $$R$$, $$d(n,R)$$ the diagonal subalgebra of $$\text{gl}(n,R)$$. In case 2 is a unit of $$R$$, all subalgebras of $$\text{gl} (n,R)$$ containing $$d(n,R)$$ are determined and their derivations are given. In case 2 is not a unit partial results are given.
##### MSC:
 13C10 Projective and free modules and ideals in commutative rings 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras 17B45 Lie algebras of linear algebraic groups
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