A cohomology theory for Lie 2-algebras and Lie 2-groups

2018/10/12 by Angulo, Camilo
#Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.05740

Abstract

In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and Lie groups in that their second groups classify extensions. We use this fact together with an adapted van Est map to prove the integrability of Lie 2-algebras anew.

Related

• Towards a new cohomology theory for strict Lie 2-groups
• The van Est homomorphism for strict Lie 2-groups
• Topologizing Lie algebra cohomology
• A new cohomology theory associated to deformations of Lie algebra morphisms
• Lie triple 2-algebras