The rational cohomology Hopf algebra of a generic Kac-Moody group

TL;DR

This paper computes the rational cohomology ring of a generic Kac-Moody group's classifying space, revealing its rational homotopy type and the Hopf algebra structure of the group.

Contribution

It provides the first explicit computation of the rational cohomology and homology Hopf algebra for generic Kac-Moody groups, advancing understanding of their topological structure.

Findings

Rational cohomology ring of the classifying space determined

Rational homotopy type of the classifying space established

Rational homology Hopf algebra of the group computed

Abstract

In this paper we determine the rational homotopy type of the classifying space of a generic Kac-Moody group by computing its rational cohomology ring. As an application we determine the rational homology Hopf algebra of the generic Kac-Moody group.