EXT GROUPS IN THE CATEGORY OF BIMODULES OVER A SIMPLE LEIBNIZ ALGEBRA

Jean Mugniery (1) , Friedrich Wagemann (2)

1 UCL - Université Catholique de Louvain = Catholic University of Louvain
2 LMJL - Laboratoire de Mathématiques Jean Leray

In this article, we generalize Loday and Pirashvili's [10] computation of the Ext-category of Leibniz bimodules for a simple Lie algebra to the case of a simple (non Lie) Leibniz algebra. Most of the arguments generalize easily, while the main new ingredient is the Feldvoss-Wagemann's cohomology vanishing theorem for semi-simple Leibniz algebras.

Mots clés: 2010]Primary 17A32; Secondary 17B56 Leibniz cohomology; Chevalley-Eilenberg cohomology; change of rings spectral sequence; cohomology vanishing; semi-simple Leibniz algebra; Whitehead theorem; Ext category of Leibniz bimodules

Domaines: Topologie algébrique [math.AT]

Jean Mugniery, Friedrich Wagemann. EXT GROUPS IN THE CATEGORY OF BIMODULES OVER A SIMPLE LEIBNIZ ALGEBRA. 2020. ⟨hal-02861691v1⟩