Report title: Cohomology of semisimple Lie- and Leibniz algebras

Reporter: Friedrich Wagemann, Université de Nantes, FRANCE

Reporting time: 15:00-16:00, December 4, 2020

Report location: Participer à la réunion Zoom

https://univ-nantes-fr.zoom.us/j/88618299866?pwd=c0I4MHZvam9ZbWUxNG9JSXk1VWllUT09

ID de réunion: 886 1829 9866

Code secret: 239126

School contact: Sheng Yunhe shengyh@jlu.edu.cn

Report summary:

The main theorem is joint work with Jörg Feldvoss (U. South Alabama, Mobile). We start by reviewing what one knows about the cohomology of semisimple Lie algebras. Then we introduce Leibniz algebras, Leibniz bimodules and the main computational tools. Afterward we report on Ntolo-Pirashvili's theorem about the Leibniz cohomology of semisimple Lie algebras. Our final topic is the Leibniz cohomology of semisimple Leibniz algebras where we show (together with Feldvoss) that all cohomology with values in a finite dimensional bimodule is zero in degree >= 2 . This shows for example that semisimple Leibniz algebras are rigid. Another application is the Ext dimension of the category of finite dimensional bimodules over a semisimple Leibniz algebra (joint work with Jean Mugniéry) which turns out to be 2.