Fractional Loop Group and Twisted K-Theory

Abstract

We study the structure of abelian extensions of the group $L_{q}G$ 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.

Final version in Commun. Math. Phys

References in corpus (1)

• Gauge invariance in fractional field theories

Cited by in corpus (1)

• Twisted K-theory, K-homology and bivariant Chern-Connes type character of some infinite dimensional spaces