## Journal of Mathematics of Kyoto University

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

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

#### 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

**Permanent link to this document**

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

Secondary: 55S10: Steenrod algebra 57T05: Hopf algebras [See also 16T05]

#### Citation

Nishimura, Osamu. On the homology of the Kac-Moody groups and the cohomology of the 3-connective covers of Lie groups. J. Math. Kyoto Univ. 42 (2002), no. 1, 175--180. doi:10.1215/kjm/1250284717. https://projecteuclid.org/euclid.kjm/1250284717