Asian Journal of Mathematics

Tame Fréchet structures for affine Kac-Moody groups

Walter Freyn

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Asian J. Math., Volume 18, Number 5 (2014), 885-928.

First available in Project Euclid: 2 December 2014

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E67: Loop groups and related constructions, group-theoretic treatment [See also 58D05] 20G44: Kac-Moody groups

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


Freyn, Walter. Tame Fréchet structures for affine Kac-Moody groups. Asian J. Math. 18 (2014), no. 5, 885--928.

Export citation