On the centre of crossed modules of groups and Lie algebras (Mariam Pirashvili)

Orateur : Mariam Pirashvili Lieu : salle des Séminaires M3 et zoom Lien zoom : https://univ-lille-fr.zoom.us/j/92282035751?pwd=QzVlNWVQZ0gvUVdXWkphNmxPVE5BQT09 Résumé : Crossed modules are algebraic models of homotopy 2-types and hence have $\pi_1$ and $\pi_2$. We propose a definition of the centre of a crossed module which is based on Drinfeld's centre for monoidal categories and whose essential invariants can be computed via the group cohomology $H^i(\pi_1; \pi_2)$. Indeed, it can be shown to be a homotopy invariant. This definition therefore has much nicer properties than one proposed by Norrie in the 80's.