Integration of Lie type algebras.Oberseminar Darstellungstheorie

by Bruno Vallette (Sorbonne)

Friday Jan 23, 2026, 12:15 PM → 2:00 PM Europe/Berlin

Endenicher Allee 60/Lipschitz-Saal (Mathezentrum)

The Baker—Campbell—Hausdorff (BCH) formula is the universal formula for integrating Lie algebras. It is however quite involved, due to the fact that it sits inside the intricate free Lie algebra for instance. For Lie brackets that come from the skew-symmetrization of binary products, one can sometimes produce more effective formulas, which admit direct applications to the deformation theory of operadic algebraic structures. For weak Lie brackets, that is L_infinity-algebras, one can use ideas from homotopy theory (Kan complexes) and rational homotopy theory (Sullivan algebras) to produce efficient higher BCH formulas. This takes the form of a universal algebraic infinity-groupoid, that is defined by a structure and not a property.