On the second cohomology group of simple Leibniz algebras
J. Q. AdashevAdashev ] Institute of Mathematics , National University of Uzbekistan , Tashkent , 100125 , UzbekistanM. LadraAdashev ] Institute of Mathematics , National University of Uzbekistan , Tashkent , 100125 , UzbekistanB. A. OmirovAdashev ] Institute of Mathematics , National University of Uzbekistan , Tashkent , 100125 , Uzbekistan
2015en
ABI
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In this paper we prove some general results on Leibniz 2-cocycles for simple Leibniz algebras. Applying these results we establish the triviality of the second Leibniz cohomology for a simple Leibniz algebra with coefficients in itself, whose associated Lie algebra is isomorphic to $\mathfrak{sl}_2$.
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