Derivations of Mackey algebras

IF 1 Q1 MATHEMATICS Carpathian Mathematical Publications Pub Date : 2023-12-28 DOI:10.15330/cmp.15.2.559-562
O. Bezushchak
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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.
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麦基代数的派生
我们描述了特征不等于 2 元的域上有限麦基代数的导数。我们证明了关联有限麦基代数或列代数 $\mathfrak{sl}_{\infty}(V|W)$, $\mathfrak{o}_\{infty}(f)$ 的任意导数是相应麦基代数中一个元素的邻接算子。它描述了巴拉诺夫-斯垂德有限简单李代数分类中所有代数的派生。证明基于雅各布森(N. Jacobson)关于无穷维向量空间线性变换关联代数的推导结果以及赫斯坦猜想的结果。
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来源期刊
CiteScore
1.90
自引率
12.50%
发文量
31
审稿时长
25 weeks
期刊最新文献
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