## Fractional Loop Group and Twisted K-Theory

##### Authors
Hekmati, Pedram
Mickelsson, Jouko
##### Description
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.
Comment: Final version in Commun. Math. Phys
##### Keywords
Mathematics - Differential Geometry, High Energy Physics - Theory, Mathematical Physics, 22E67, 55N15, 81T60