On the Stiefel-Whitney class of the adjoint representation of \(E_8\)
type: Item
instance of: scholarly article
title: On the Stiefel-Whitney class of the adjoint representation of \(E_8\)
zbMATH Open document ID: 1069.57021
author: Akihiro Ohsita
published in: Proceedings of the Japan Academy. Series A
publication date: 2005-04-04T00:00:00Z
review text: Let \(\widetilde{E_8}\) be the \(3\)-connected covering space of the simply connected Lie group \(E_8\). Let \(\pi_8: \widetilde{E_8} \to E_8\) be the covering map and \(\pi_8^*: H^*(Be_8) \to H^*(B\widetilde{E_8})\) be the induced map between the \(\mathbb{Z}_2\) cohomology of the classifying spaces. The main result (Theorem 4) computes the images of the \(2^i\)th Stiefel--Whitney class of the adjoint representation of \(E_8\) under \(\pi_8^*\) for \(i\leq7\). The article contains only a sketch of proof; the author postpones the proof to another paper. This sketch is an explicit calculation using an explicit expression for the cohomology rings and some maps, and applying the Steenrod operations.
reviewed by: Gábor Braun
Mathematics Subject Classification ID: 57T10
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 2151800
zbMATH Keywords: Stiefel--Whitney class
zbMATH Keywords: classifying space
zbMATH Keywords: exceptional Lie group
zbMATH Keywords: adjoint representation
MaRDI profile type: Publication
full work available at URL: pjaa.80.155
OpenAlex ID: W1970351048
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DOI: 10.3792/PJAA.80.155
description: scientific article; zbMATH DE number 2151800