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Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings

Deng Yin Wang, Xian Wang (2008)

Archivum Mathematicum

Let R be an arbitrary commutative ring with identity, gl ( n , R ) the general linear Lie algebra over R , d ( n , R ) the diagonal subalgebra of gl ( n , R ) . In case 2 is a unit of R , all subalgebras of 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.

Generalized derivations of Lie triple systems

Jia Zhou, Liangyun Chen, Yao Ma (2016)

Open Mathematics

In this paper, we present some basic properties concerning the derivation algebra Der (T), the quasiderivation algebra QDer (T) and the generalized derivation algebra GDer (T) of a Lie triple system T, with the relationship Der (T) ⊆ QDer (T) ⊆ GDer (T) ⊆ End (T). Furthermore, we completely determine those Lie triple systems T with condition QDer (T) = End (T). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.

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