Derivations of Mackey algebras - Bezushchak, O. (Carpathian Mathematical Publications, 2023)
We describe derivations of finitary Mackey algebras over fields of characteristics not equal to 2. We prove that an arbitrary derivation of an associative finitary Mackey algebra or one of the Lie algebras sl_∞(V|W), o_∞(f) is an adjoint operator of an element in the corresponding Mackey algebra. It provides a description of the derivations of all algebras in the Baranov-Strade classification of finitary simple Lie algebras. The proof is based on N. Jacobson's result on derivations of associative algebras of linear transformations of an infinite-dimensional vector space and the results on Herstein's conjectures.