Infinite loop spaces associated to affine Kac-Moody groups

TL;DR

This paper extends the construction of infinite loop spaces, previously known for classical groups over rings, to the broader context of affine Kac-Moody groups, enriching the algebraic topology framework.

Contribution

It generalizes the association of infinite loop spaces via Quillen's plus construction from classical groups to affine Kac-Moody groups, a significant theoretical advancement.

Findings

Established a method to associate infinite loop spaces to affine Kac-Moody groups

Extended Quillen's plus construction to a new class of infinite-dimensional groups

Provided a foundation for further topological and algebraic studies of Kac-Moody groups

Abstract

It is well known that to each infinite class of classical groups over a commutative ring $R$, we can associate an infinite loop space by Quillen's plus construction. In this paper we generalize this fact to the case of affine Kac-Moody groups.