#### Conference abstracts

Session A5 - Geometric Integration and Computational Mechanics

July 11, 17:30 ~ 18:00 - Room 111

## Action algebroids are the only post-Lie algebroids

### Ari Stern

### Washington University in St. Louis, USA - stern@wustl.edu

Despite their name, Lie group integrators may also be applied to certain manifolds that are not Lie groups: homogeneous spaces, for example. In general, Munthe-Kaas and Lundervold showed that Lie-Butcher series methods may be defined on vector bundles called post-Lie algebroids. We show that every post-Lie algebroid arises from a Lie algebra action, meaning that manifolds with Lie algebra actions are essentially the most general spaces to which Lie-Butcher series methods may be applied.

Joint work with Hans Z. Munthe-Kaas (University of Bergen) and Olivier Verdier (Bergen University College).