Lie 2-groups from loop group extensions

2023/03/23 by Matthias Ludewig, Ludewig, Matthias, Konrad Waldorf +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2303.13176

openalex publication_date 2023/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions

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