Ext groups in the category of bimodules over a simple Leibniz algebra

TL;DR

This paper extends the computation of Ext groups from Leibniz bimodules over simple Lie algebras to simple Leibniz algebras, utilizing cohomology vanishing theorems for semi-simple cases.

Contribution

It generalizes previous Ext-category computations to non-Lie Leibniz algebras, introducing new applications of cohomology vanishing theorems.

Findings

Extended Ext group computations to simple Leibniz algebras.

Utilized Feldvoss-Wagemann's cohomology vanishing theorem.

Simplified arguments from the Lie algebra case to Leibniz algebra case.

Abstract

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.