# The Drinfel'd centres of String 2-groups

@inproceedings{Weis2022TheDC, title={The Drinfel'd centres of String 2-groups}, author={Christoph Weis}, year={2022} }

Let G be a compact connected Lie group and k ∈ H4(BG,Z) a cohomology class. The String 2-group Gk is the central extension of G by the 2-group [∗/U(1)] classified by k. It has a close relationship to the level k extension of the loop group LG. We compute the Drinfel’d centre of Gk as a smooth 2-group. When G is simplyconnected, it is the invertible part of the category of positive energy representations of LG at level k.

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