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Journal of Lie Theory 23 (2013), No. 3, 699--709
Copyright Heldermann Verlag 2013

Infinite Loop Spaces Associated to Affine Kac-Moody Groups

Xianzu Lin
College of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350108, China

The main purpose of this paper is to construct infinite loop spaces from affine Kac-Moody groups, It is well known that to each infinite class of classical groups over a commutative ring R, we can associate an infinite loop space G(R) by Quillen's plus construction. In this paper we generalize this fact to the cases of affine Kac-Moody groups. Roughly speaking, for each commutative ring R there are seven infinite classes of affine Kac-Moody groups over R, and to each infinite class we can associate an analogous infinite loop space.

Keywords: Infinite loop space, affine Kac-Moody group.

MSC: 55P47, 20G44

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