Towards a new cohomology theory for strict Lie 2-groups

TL;DR

This paper develops a novel cohomology theory for strict Lie 2-groups, extending classical Lie group cohomology and providing a framework for classifying extensions.

Contribution

It introduces the first degrees of a cochain complex for strict Lie 2-groups, extending classical cohomology and suggesting possible higher-degree generalizations.

Findings

Second cohomology classifies extensions of strict Lie 2-groups.

The cochain complex extends classical Lie group cohomology.

Evidence suggests the complex can be extended to all degrees.

Abstract

In this article, we introduce the first degrees of a cochain complex associated to a strict Lie 2-group whose cohomology is shown to extend the classical cohomology theory of Lie groups. In particular, we show that the second cohomology group classifies an appropriate type of extension. We conclude by putting forward evidence that this complex can be extended to arbitrary degrees.