Polynomial algebras over the Steenrod algebra
type: Item
instance of: scholarly article
title: Polynomial algebras over the Steenrod algebra
zbMATH Open document ID: 0716.55016
DOI: 10.1007/BF02566601
author: H. E. A. Campbell
author: Paul Selick
published in: Commentarii Mathematici Helvetici
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140189
review text: Let H denote the mod p cohomology of B(\({\mathbb{Z}}/p{\mathbb{Z}})\), considered as an object in the category \({\mathcal U}\) of unstable modules over the mod p Steenrod algebra A. It is proved that \(H^{\otimes s}\) is isomorphic to \(F_ 2[x_ 1,...,x_ s]\) with A-action given by \(Sq^ 1x_ j=x^ 2_{j-1}\). This is used to obtain a nice A-module decomposition of \(H^{\otimes s}\), and to reprove its \({\mathcal U}\)-injectivity.
Mathematics Subject Classification ID: 55S10
zbMATH DE Number: 4180330
zbMATH Keywords: mod p cohomology
zbMATH Keywords: unstable modules
zbMATH Keywords: mod p Steenrod algebra
zbMATH Keywords: injectivity
MaRDI profile type: Publication
OpenAlex ID: W1967593251
description: scientific article; zbMATH DE number 4180330