Abstract

In this article, we discuss completeness of non-Lie Leibniz algebras by studying various conditions under which they admit outer derivations. Our study focusses particularly on the class of non-perfect Leibniz algebras whose center is not contained in the Leibniz kernel. We extend to this class of Leibniz algebras several well-known results on derivations of Lie algebras. In particular, we show that solvable Leibniz algebras in this class are not complete. Also, we show that non-stem Leibniz algebras admit outer central derivations. Finally, we independently show that semisimple non-Lie Leibniz algebras are complete.

中文翻译：

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关于莱布尼兹代数外推导的注记

摘要

在本文中，我们将通过研究非李莱布尼兹代数接受外部导数的各种条件来讨论其完备性。我们的研究特别关注中心不包含在Leibniz核中的非完美Leibniz代数的类别。我们将有关Lie代数导数的一些著名结果扩展到此类Leibniz代数。特别是，我们证明了此类中的可解决的莱布尼兹代数不完整。此外，我们证明了非茎Leibniz代数接受外部中心导数。最后，我们独立地证明半简单的非李·莱布尼兹代数是完整的。