The Drinfel'd centres of String 2groups
Abstract
Let $G$ be a compact connected Lie group and $k \in H^4(BG,\mathbb{Z})$ a cohomology class. The String 2group $G_k$ is the central extension of $G$ by the 2group $[\ast/U(1)]$ 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 $G_k$ as a smooth 2group. When $G$ is simplyconnected, it is the invertible part of the category of positive energy representations of $LG$ at level $k$.
 Publication:

arXiv eprints
 Pub Date:
 February 2022
 arXiv:
 arXiv:2202.01271
 Bibcode:
 2022arXiv220201271W
 Keywords:

 Mathematics  Representation Theory;
 Mathematical Physics;
 Mathematics  Category Theory;
 Mathematics  Quantum Algebra