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Derivations of the parabolic subalgebras of the general linear Lie algebra over a commutative ring. (English) Zbl 1161.17313
Summary: Let \(R\) be an arbitrary commutative ring with identity, \(\text{gl}(n, R)\) the general linear Lie algebra over \(R\). The aim of this paper is to give an explicit description of the derivation algebras of the parabolic subalgebras of \(\text{gl}(n, R)\).

MSC:
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
16W25 Derivations, actions of Lie algebras
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[1] Cao, Y., Automorphisms of certain Lie algebras of upper triangular matrices over a commutative ring, J. algebra, 189, 506-513, (1997) · Zbl 0878.17016
[2] Cao, Y., Automorphisms of Lie algebras of strictly upper triangular matrices over certain commutative rings, Linear algebra appl., 329, 175-187, (2001) · Zbl 0987.17010
[3] Cao, Y.; Tang, Z., Automorphisms of the Lie algebras of strictly upper triangular matrices over a commutative ring, Linear algebra appl., 360, 105-122, (2003) · Zbl 1015.17017
[4] Jøndrup, S., Automorphisms and derivations of upper triangular matrix rings, Linear algebra appl., 221, 205-218, (1995) · Zbl 0826.16034
[5] Jøndrup, S., The group of automorphisms of certain subalgebras of matrix algebras, J. algebra, 141, 106-114, (1991) · Zbl 0729.16024
[6] Jøndrup, S., Automorphisms of upper triangular matrix rings, Arch. math., 49, 497-502, (1987) · Zbl 0601.16028
[7] Benkart, G.M.; Osbom, J.M., Derivations and automorphisms of non-associative matrix algebras, Trans. amer. math. soc., 263, 411-430, (1981) · Zbl 0453.16020
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