On unstable modules over the Dickson algebras, the Singer functors \(R_{s}\) and the functors \(Fix_{S}\)
type: Item
instance of: scholarly article
title: On unstable modules over the Dickson algebras, the Singer functors \(R_{s}\) and the functors \(Fix_{S}\)
zbMATH Open document ID: 1263.55004
published in: Algebraic \& Geometric Topology
publication date: 2013-02-25T00:00:00Z
review text: This paper continues the author's work [J. Pure Appl. Algebra 214, No. 8, 1435--1449 (2010; Zbl 1186.55009)] on unstable modules and Singer's functor \(R_s\) from the category \(\mathcal{U}\) of unstable modules over the mod \(2\) Steenrod algebra to the category \(D_s-\mathcal{U}\) of unstable modules equipped with an action of the Dickson algebra \(D_s\) [\textit{W. M. Singer}, Math. Proc. Camb. Philos. Soc. 90, 279--292 (1981; Zbl 0479.55013)]. An approximation \(\tilde{R}_s\) of \(R_s\) is given, and used in proving that the natural transformation of functors on \(\mathcal{U}\), from \(\text{Fix}_s(H^*V_s \otimes_{D_s} R_s(-))\) to \(1_{\mathcal U}\), is an isomorphism for all natural numbers \(s\). This implies that \(R_s\) gives a fully-faithful embedding of \(\mathcal{U}\) in \(D_s-\mathcal{U}\).
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 18E10
zbMATH DE Number: 6138568
zbMATH Keywords: Dickson algebra
zbMATH Keywords: Singer functor
zbMATH Keywords: unstable module
zbMATH Keywords: Lannes' \(T\)-functor
zbMATH Keywords: Fix
author: Geoffrey Powell
reviewed by: Martin D. Crossley
MaRDI profile type: Publication
full work available at URL: agt.2012.12.2451
OpenAlex ID: W2059006897
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DOI: 10.2140/AGT.2012.12.2451
description: scientific article; zbMATH DE number 6138568