ON LEIBNIZ COHOMOLOGY

Jörg Feldvoss (1) , Friedrich Wagemann (2)

1 University of South Alabama
2 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Domaines: Topologie algébrique [math.AT]

Jörg Feldvoss, Friedrich Wagemann. ON LEIBNIZ COHOMOLOGY. 2019. ⟨hal-02017136v1⟩