On complete Leibniz algebras
Sh. A. AyupovNational University of Uzbekistan, University Street, 4, Tashkent 100174, UzbekistanAbror KhudoyberdiyevNational University of Uzbekistan, University Street, 4, Tashkent 100174, UzbekistanZarina ShermatovaV.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, University Street, 9, Tashkent 100174, Uzbekistan
ABI
Аннотация
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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