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Derivation algebra of direct sum of Lie algebras. (English) Zbl 1427.17043

Summary: Let \(L_1\) and \(L_2\) be two finite dimensional Lie algebras on arbitrary field F with no common direct factor and \(L=L_1\otimes L_2\). In this article, we express the structure and dimension of derivation algebra of \(L, \mathrm{Der}(L)\), and some of their subalgebras in terms of \(\mathrm{Der}(L_1)\), \(\mathrm{Der}(L_2)\), \(\mathrm{Hom}(L_1,Z(L_2))\), and \(\mathrm{Hom}(L_2,Z(L_1))\).

MSC:

17B99 Lie algebras and Lie superalgebras
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