Non-integral central extensions of loop groups

Details Non-integral central extensions of loop groups Non-integral central extensions of loop groups

2009-10-10

arxiv.org/abs/0910.1937v1

Contemp. Math. 519 (2010) 203-214

Physics

Mathematical Physics

12 pages, final version, to appear in Contemp. Math

Scientific paper

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.

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