弦2-群的Drinfel'd中心
The Drinfel'd centres of String 2-groups
摘要：
设$G$是紧连通李群，$k \in H^4(BG,\mathbb{Z})$是上同调类. String 2-group $G_k$是由$k$分类的2-group $[\ast/U(1)]$对$G$的中心扩展。它与循环组$LG$的级别$k$扩展有密切关系。我们把$G_k$的Drinfel'd中心计算为光滑2-群.当$G$是半单的时候，我们证明了Drinfel'd中心等于$G$在$k$层的正能量表示范畴的可逆部分（只要我们排除$E_8$在2层的因子）.
英文摘要：
Let $G$ be a compact connected Lie group and $k \in H^4(BG,\mathbb{Z})$ a cohomology class. The String 2-group $G_k$ is the central extension of $G$ by the 2-group $[\ast/U(1)]$ 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 2-group. When $G$ is semisimple, we prove that the Drinfel'd centre is equal to the invertible part of the category of positive energy representations of $LG$ at level $k$ (as long as we exclude factors of $E_8$ at level 2).
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