Contact Lie algebras and generic stabilisers

par Oksana Yakimova (Univ Jena)

jeudi 5 mars 2026, 11:15 → 12:15 Europe/Paris

Batiment des Forges (Saint-Etienne (site de manufacture))

Contact geometry is an odd-dimensional version of the symplectic one. An odd-dimensional Lie group Q has an invariant contact structure if and only if its Lie algebra is contact. In that case, a generic coadjoint orbit of Q is of codimension 1, i.e., the index of $Lie Q$ is 1. The latter condition is necessary, but not sufficient.  We show that a Lie algebra of index 1 is contact if and only if there is a generic stabiliser for the coadjoint action.