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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.
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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