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Almost inner derivations of Lie superalgebras
Vera Serganova, Arkady Vaintrob
https://arxiv.org/abs/2509.00689 https://arxiv.org/pdf/2509.00689

Almost inner derivations of Lie superalgebras
An almost inner derivation of a Lie algebra $L$ is a derivation that coincides with an inner derivation on each one-dimensional subspace of $L$. The almost inner derivations form a subalgebra ${aDer}(L)$ of the Lie algebra ${Der}(L)$ of all derivations of $L$, containing the inner derivations ${iDer}(L)$ as an ideal. If $L$ is a simple finite-dimensional Lie algebra, then ${aDer}(L)={iDer}(L)$, since all derivations of $L$ are inner. In this paper, we introduce and study almost inner derivati…