## Derivations of the intermediate Lie algebras between the Lie algebra of diagonal matrices and that of upper triangular matrices over a commutative ring.(English)Zbl 1161.17312

Summary: Let $$R$$ be an arbitrary commutative ring with identity, $$\text{gl}(n, R)$$ the general linear Lie algebra over $$R$$ consisting of all $$n\times n$$ matrices over $$R$$ and with the bracket operation $$[x, y] = xy - yx$$, $$\mathbf t$$ (resp., $$\mathbf u$$) the Lie subalgebra of $$\text{gl}(n, R)$$ consisting of all $$n\times n$$ upper triangular (resp., strictly upper triangular) matrices over $$R$$ and $$\mathbf d$$ the Lie subalgebra of $$\text{gl}(n, R)$$ consisting of all $$n\times n$$ diagonal matrices over $$R$$. The aim of this article is to give an explicit description of the derivation algebras of the intermediate Lie algebras between $$\mathbf d$$ and $$\mathbf t$$.

### MSC:

 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
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### References:

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