Derivations, local and 2-local derivations and automorphism groups of 3-dimensional nilpotent Lie-Yamaguti algebras

In this paper, we study derivations, automorphisms, and their local and 2-local analogues on 3-dimensional nilpotent Lie–Yamaguti algebras over a field F of characteristic zero. Based on the known classification of such algebras, we explicitly compute their derivation algebras and automorphism groups. We further describe the matrix forms of local derivations and local automorphisms. Our results show that, for the non-abelian algebras under consideration, local derivations and local automorphisms form strictly larger classes than ordinary derivations and automorphisms, respectively. In addition, we construct 2-local derivations which are not derivations and 2-local automorphisms which are not automorphisms.

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