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
linxianzu@126.com
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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