Derivations of Mackey algebras
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Published:2023-12-28
Issue:2
Volume:15
Page:559-562
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ISSN:2313-0210
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Container-title:Carpathian Mathematical Publications
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language:
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Short-container-title:Carpathian Math. Publ.
Abstract
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 $\mathfrak{sl}_{\infty}(V|W)$, $\mathfrak{o}_{\infty}(f)$ is an adjoint operator of an element in the corresponding Mackey algebra. It provides description of 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.
Publisher
Vasyl Stefanyk Precarpathian National University
Subject
General Mathematics