论文标题
弦2组的drinfel'd中心
The Drinfel'd centres of String 2-groups
论文作者
论文摘要
令$ g $为h^4（bg，\ mathbb {z}）$ cohomology类中的紧凑型谎言组和$ k \。字符串2组$ g_k $是由$ k $分类的2 group $ [\ ast/u（1）] $的$ g $的中心扩展。它与Loop Group $ LG $的级$ K $扩展相关。我们将$ g_k $的Drinfel'd中心视为平滑的2组。当$ g $是半imple时，我们证明了drinfel'd中心等于$ k $ $ lg $的$ lg $类别的可逆部分（只要我们排除了2级$ e_8 $的因素）。
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).
