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

TL;DR

This thesis develops new cohomology theories for Lie 2-algebras and Lie 2-groups, extending classical theories and providing tools for their classification and integration.

Contribution

It introduces novel cohomology theories for Lie 2-algebras and Lie 2-groups, extending classical concepts and enabling classification of extensions and integrability.

Findings

Cohomology theories extend classical Lie algebra and group cohomology.

Second cohomology groups classify extensions of Lie 2-algebras and Lie 2-groups.

An adapted van Est map proves the integrability of Lie 2-algebras.

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.