On the second cohomology group of simple Leibniz algebras

2015/02/02 by J. Q. Adashev, Adashev, J. Q., M. Ladra +3
Mathematics · #16E40 #17A32 #17A36 #17B20 #17B40 #17B56 #57T10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1502.00609

openalex publication_date 2015/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \mathfraksl₂.

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