Lie 2-groups from loop group extensions

Matthias Ludewig; Konrad Waldorf

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arXiv · 2303.13176

Lie 2-groups from loop group extensions

Matthias Ludewig·Konrad Waldorf

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Abstract

We give a very simple construction of the string 2-group as a strict Fr\'echet 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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BibTeX RIS

Matthias Ludewig, Konrad Waldorf. 2023-03-23. Lie 2-groups from loop group extensions. https://arxiv.org/abs/2303.13176

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