07/12/2017, 16:00 — 17:00 — Room P4.35, Mathematics Building
Rui Loja Fernandes, University of Illinois at Urbana-Champaign
Associativity and Integrability
A classical theorem by Mal'cev shows that the only obstruction to embedd a local Lie group to a global Lie group is the failure of (higher) associativity. A theorem of Olver characterizes local Lie groups in terms of Lie groups. We show that both results can be generalized to the setting of local Lie groupoids. More important, we show that (the lack of) associativity is intimately connected to (the lack of) integrability: we give a precise connection in the case of Lie algebroids and we conjecture that it holds also for reasonable infinite dimensional Lie algebras (e.g., Banach Lie algebras). This is joint work with my PhD student Daan Michiels.