Integrating Lie 2-algebras

Speaker: Camilo Angulo, UFF.

Date: 06 sep 2019, 11h.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: A Lie 2-algebra is a groupoid object in the category of Lie algebras. These can naturally be seen as an infinitesimal version of Lie 2-groups which are groupoids in the category of Lie groups. Lie 2-algebras are known to be integrable in this sense. To understand this integration process from a cohomological point of view, we present appropriate notions of representations for both Lie 2-groups and Lie 2-algebras and the corresponding complexes whose cohomologies classify extensions. Finally, we discuss a van Est type theorem.