## Journal of Mathematics of Kyoto University

### On the homology of the Kac-Moody groups and the cohomology of the 3-connective covers of Lie groups

Osamu Nishimura

#### Abstract

Let $G$ be a compact, 1-connected, simple Lie group of exceptional type, $g$ its Lie algebra, and $p$ an odd prime. In this paper, the mod $p$ homology of the Kac-Moody group $K(g^{(1)})$ and the mod $p$ cohomology of the 3-connective cover over $G$ are determined as Hopf algebras over the Steenrod algebra for every case that the integral homology of $G$ has $p$-torsion.

#### Article information

Source
J. Math. Kyoto Univ., Volume 42, Number 1 (2002), 175-180.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250284717

Digital Object Identifier
doi:10.1215/kjm/1250284717

Mathematical Reviews number (MathSciNet)
MR1932743

Zentralblatt MATH identifier
1027.57033

Subjects
Primary: 57T10: Homology and cohomology of Lie groups