loop群的非整中心扩张
Non-integral central extensions of loop groups
摘要：
众所周知，紧致单1-连通李群的loop群的中心扩张由它们的水平$k \in Z$参数化。本文关注的问题有多少可以说任意$k \in R$和我们表明，对于每个$k$存在一个李群胚的水平$k$中心扩展作为其商，如果$k \in Z$。通过考虑范畴化的主丛，我们还证明了相应的李群胚具有期望的丛结构。
英文摘要：
It is well-known that the central extensions of the loop group of a compact, simple and 1-connected Lie group are parametrised by their level $k \in Z$. This article concerns the question how much can be said for arbitrary $k \in R$ and we show that for each $k$ there exists a Lie groupoid which has the level $k$ central extension as its quotient if $k \in Z$. By considering categorified principal bundles we show, moreover, that the corresponding Lie groupoid has the expected bundle structure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
