The \(\text{mod }3\) homology of the space of loops on the exceptional Lie groups and the adjoint action
type: Item
instance of: scholarly article
title: The \(\text{mod }3\) homology of the space of loops on the exceptional Lie groups and the adjoint action
zbMATH Open document ID: 0912.57023
author: Hiroaki Hamanaka
author: Shin-ichiro Hara
published in: Journal of Mathematics of Kyoto University
publication date: 1998-11-05T00:00:00Z
review text: The title of this paper accurately describes its contents -- the determination of the homology of the loop space \(\Omega G\) at the prime 3, where \(G\) is one of the five exceptional Lie groups, together with the induced adjoint action. the results are motivated by R. Bott's theorem that \(H*(\Omega G, \mathbb{Z}/p)\) is a finitely-generated bicommutative Hopf algebra, generated in even degrees, and his determination of this algebra when \(G\) belongs to one of the families of classical groups. The main additional ingredient needed is the (co)homology of the groups concerned, which to a large extent is labeled by the exponents of the group. We must also remember that in most cases the prime 3 also divides the order of the Weyl group.
Mathematics Subject Classification ID: 57T10
zbMATH DE Number: 1189511
zbMATH Keywords: cohomology of specific Lie groups and spaces
Wikidata QID: Q115240436
reviewed by: Charles B. Thomas
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518265
OpenAlex ID: W1700645207
DOI: 10.1215/KJM/1250518265
description: scientific article; zbMATH DE number 1189511