Fractional Loop Group and Twisted K-Theory

Details Fractional Loop Group and Twisted K-Theory Fractional Loop Group and Twisted K-Theory

2008-01-16

arxiv.org/abs/0801.2522v4

Commun.Math.Phys.299 (3):741-763,2010

Mathematics

Differential Geometry

Final version in Commun. Math. Phys

Scientific paper

10.1007/s00220-010-1108-6

We study the structure of abelian extensions of the group $L_qG$ of $q$-differentiable loops (in the Sobolev sense), generalizing from the case of central extension of the smooth loop group. This is motivated by the aim of understanding the problems with current algebras in higher dimensions. Highest weight modules are constructed for the Lie algebra. The construction is extended to the current algebra of supersymmetric Wess-Zumino-Witten model. An application to the twisted K-theory on $G$ is discussed.

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