Abstract
We study derivations of ternary Lie algebras. Precisely, we investigate the relation between derivations of Lie algebras and the induced ternary Lie algebras. We also explore the spaces of quasi-derivations, the centroid and the quasi-centroid and give some properties. Finally, we compute these spaces for low dimensional ternary Lie algebras g.
Highlights
Derivations of different algebraic structures are an important subject of study in algebra and diverse areas
They appear in many fields of mathematics and physics
In the present paper we are interested in studying the derivations of Lie algebras and derivations of induced ternary Lie algebras
Summary
Derivations of different algebraic structures are an important subject of study in algebra and diverse areas. Space Der(g) and other subspaces, we give their properties and study the connection between derivations of Lie algebras and induced ternary Lie algebras. Given two ternary Lie algebras (g, [·, ·, ·]) and (η, [·, ·, ·]η), the space g ⊕ η with the bracket defined by Let (g, [·, ·, ·]) be a ternary Lie algebra, and D a linear map on g.
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