The second cohomology group of simple Leibniz algebras
J. Q. AdashevInstitute of Mathematics, National University of Uzbekistan, Tashkent 100125, UzbekistanM. LadraDepartment of Algebra, University of Santiago de Compostela, La Coruña 15782, SpainB. A. OmirovInstitute of Mathematics, National University of Uzbekistan, Tashkent 100125, Uzbekistan
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In this paper, we prove some general results on Leibniz 2-cocyles for simple Leibniz algebras. Applying these results, we prove the triviality of the second Leibniz cohomology for a simple Leibniz algebra with coefficients in itself, whose associated Lie algebra is isomorphic to [Formula: see text].
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