Work

Lie 2-groups from loop group extensions

Year: 2024

Type: article

Abstract: We give a very simple construction of the string 2-group as a strict Fréchet Lie 2-group. The corresponding crossed module is defined using the conjugation action of the loop group on its central extension, which drastically simplifies several constructions previously given in the literature. More generally, we construct strict 2-group extensions for a Lie group from a central extension of its based loop group, under the assumption that this central extension is disjoint commutative. We show in particular that this condition is automatic in the case that the Lie group is semisimple and simply connected.

Source: Journal of Homotopy and Related Structures

DOI: 10.1007/s40062-024-00355-4

Authors: Matthias Ludewig, Konrad Waldorf

Institutions: University of Regensburg, Universität Greifswald

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Deutsche Forschungsgemeinschaft, Universität Regensburg