Almost inner derivations of finite-dimensional simple Leibniz algebras

UDC 512.5 We study almost inner derivations of finite-dimensional simple Leibniz algebras. First, we examine almost inner derivations of the simple Leibniz algebra $\mathfrak{sl}_2\ltimes\mathcal{I}$ and prove that every derivation of this kind is inner. Furthermore, we analyze almost inner derivations of other simple Leibniz algebras and show that the existence of almost inner derivations that are not inner is possible only in cases other than $\mathfrak{sl}_2.$

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