ON LEIBNIZ COHOMOLOGY
Résumé
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.
Mots clés
November 3
2020. 2010 Mathematics Subject Classification. Primary 17A32
Secondary 17B56 Leibniz cohomology
Chevalley-Eilenberg cohomology
spectral sequence
cohomological vanishing
invariant symmetric bilinear form
Cartan-Koszul map
complete Lie algebra
rigid Leibniz algebra
Witt algebra
Borel subalgebra
parabolic subalgebra
semi-simple Leibniz algebra
second Whitehead lemma
outer derivation
Domaines
Topologie algébrique [math.AT]
Origine : Fichiers produits par l'(les) auteur(s)