Symmetries of singular foliations and Lie infinity actions
- Event Type
- Seminar/Symposium
- Sponsor
- Ely Kerman
- Location
- 243 Altgeld Hall
- Date
- Sep 8, 2025 4:00 - 4:50 pm
- Speaker
- Reuben Louis (UIUC)
- Contact
- Ely Kerman
- ekerman@illinois.edu
- Views
- 53
Abstract: We investigate singular foliations that admit a universal Lie infinity-algebroid, as defined by Laurent-Gengoux, Lavau, and Strobl.
We prove that any weak symmetry action of a Lie algebra g on a singular foliation (M,F)—Such an action can be understood as an action of g on the leaf space M/F—induces a unique (up to homotopy) Lie infinity-morphism from g to the differential graded Lie algebra (DGLA) of vector fields on the universal Lie infinity-algebroid of F. This type of Lie infinity-morphism, previously explored by R. Mehta and M. Zambon as a Lie infinity-algebra action, yields several geometric insights. As a specific instance, we give an example of a Lie algebra action on an affine sub-variety which cannot be extended on the ambient space.