Jörg Feldvoss, Friedrich Wagemann
Published 2019-02-16Version 1
In this paper we prove the Leibniz analogues of several vanishing theorems for the Chevalley-Eilenberg cohomology of Lie algebras. In particular , we obtain the second Whitehead lemma for Leibniz algebras. Our main tools are three spectral sequences. Two are Leibniz analogues of the Hochschild-Serre spectral sequence, one of which is an extension of the dual of a spectral sequence of Pirashvili for Leibniz homology from symmetric bi-modules to arbitrary bimodules, and the other one is due to Beaudouin. A third spectral sequence (also due to Pirashvili in homology) relates the Leibniz cohomology of a Lie algebra to its Chevalley-Eilenberg cohomology.
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