Article

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

International Journal of Algebra and Computationjournal2022en

ABI

Abstract

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.

Topics

Advanced Topics in Algebra Algebraic structures and combinatorial models Homotopy and Cohomology in Algebraic Topology

Identifiers

DOI: 10.1142/s0218196722500138

Citations and references

Cited by 4 11 references

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