Asian Journal of Mathematics

Volume 18 (2014)

Number 5

Tame Fréchet structures for affine Kac-Moody groups

Pages: 885 – 928



Walter Freyn (Fachbereich Mathematik, Technische Universität Darmstadt, Germany)


We construct holomorphic loop groups and their associated affine Kac-Moody groups and prove that they are tame Fréchet manifolds; furthermore we study the adjoint action of these groups. These results form the functional analytic core for a theory of affine Kac-Moody symmetric spaces, that will be developed in forthcoming papers. Our construction also solves the problem of complexification of completed Kac-Moody groups: we obtain a description of complex completed Kac-Moody groups and, using this description, deduce constructions of their non-compact real forms.


loop group, loop algebra, affine Kac-Moody group, affine Kac-Moody algebra, tame Fréchet space, completion

2010 Mathematics Subject Classification

20G44, 22E67

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