Communications in Mathematical Physics

, Volume 299, Issue 3, pp 741–763 | Cite as

Fractional Loop Group and Twisted K-Theory

  • Pedram Hekmati
  • Jouko Mickelsson


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 the 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 the supersymmetric Wess-Zumino-Witten model. An application to the twisted K-theory on G is discussed.


Central Extension Verma Module Loop Group Loop Algebra Left Invariant Vector 
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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsRoyal Institute of TechnologyStockholmSweden
  2. 2.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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