Martes 06/08/2024, 16.00 hs. Aula 27
Titulo: Affine actions: from Milnor’s question to post-Lie algebra structures
Resumen:
In 1977, Milnor posed the question whether every simply connected and connected solvable Lie group admits a simple transitive action on R^n by affine transformation. Although there were some positive results for nilpotent groups of low nilpotency class, almost 20 years later Benoist constructed a first counterexample. However, it is known that Milnor’s question has a positive answer if one replaces R^n by a suitable nilpotent Lie group H, depending on G.
Not much is known about which pairs of Lie groups (G,H) admit such an action, where ideally you only need information about the Lie algebras corresponding to G and H. In recent work with Marcos Origlia, we show that every simply transitive action induces a post-Lie algebra structure on the corresponding Lie algebras. Moreover, if H has nilpotency class 2 we characterize the post-Lie algebra structures coming from such an action by giving a new definition of completeness, extending the known cases where G is nilpotent or H is abelian.