关于完全莱布尼兹代数

Sh. A. Ayupov, A. Khudoyberdiyev, Z. Shermatova
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引用次数: 0

摘要

本文致力于研究所谓的完全莱布尼兹代数。构造了具有完全根的完全莱布尼兹代数,并证明了完全莱布尼兹代数的直和也是完全的。已知具有完全理想的李代数是分裂的。我们讨论了这一结果在莱布尼兹代数上的类似情形,并证明了它对某些特殊的莱布尼兹代数是成立的。最后,我们考虑了莱布尼兹代数的导数,并给出了一些不完备的莱布尼兹代数,因为它们允许外导。
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On complete Leibniz algebras
This paper is devoted to the so-called complete Leibniz algebras. We construct some complete Leibniz algebras with complete radical and prove that the direct sum of complete Leibniz algebras is also complete. It is known that a Lie algebra with a complete ideal is split. We discuss the analogs of this result for the Leibniz algebras and show that it is true for some special classes of Leibniz algebras. Finally, we consider derivations of Leibniz algebras and present some classes of Leibniz algebras which are not complete, since they admit outer derivation.
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