Asian Journal of Mathematics

Tame Fréchet structures for affine Kac-Moody groups

Walter Freyn

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Abstract

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

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

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1417489246

Mathematical Reviews number (MathSciNet)
MR3287007

Zentralblatt MATH identifier
1311.22029

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

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

Citation

Freyn, Walter. Tame Fréchet structures for affine Kac-Moody groups. Asian J. Math. 18 (2014), no. 5, 885--928. https://projecteuclid.org/euclid.ajm/1417489246


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