The study establishes conditions under which 2-local inner derivations exhibit unique behaviors in specific Lie algebras, suggesting deeper algebraic structures.
We establish that every 2-local inner derivation on a symmetrizable Kac-Moody Lie algebra [Formula: see text] over the field [Formula: see text] is a derivation. In addition, we demonstrate that if [Formula: see text], where [Formula: see text] is the derived subalgebra of [Formula: see text], then [Formula: see text] admits a 2-local derivation which is not a derivation.
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Nehra et al. (2026) studied this question.
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