Derivation subalgebras of Lie algebras

doi:10.1285/i15900932v38n2p105

Derivation subalgebras of Lie algebras

F. Saeedi, S. Sheikh-Mohseni

Abstract

Let $L$ be a Lie algebra and $I,$ $J$ be two ideals of $L$ . If $\Der_J^I(L)$ denotes the set of all derivations of $L$ whose images are in $I$ and send $J$ to zero, then we give necessary and sufficient conditions under which $\Der_J^I(L)$ is equal to some special subalgebras of the derivation algebra of $L$ . We also consider finite dimensional Lie algebra for which the center of the set of inner derivations, $Z(\IDer(L))$ , is equal to the set of central derivations of $L$ , $\Der_z(L)$ , and give a characterisation of such Lie algebras.

DOI Code: 10.1285/i15900932v38n2p105

Keywords: Derivation; central derivation; inner derivation

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This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.

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Note di Matematica

Derivation subalgebras of Lie algebras

Abstract