Polynomial filtrations and Lannes' \(T\)-functor
type: Item
instance of: scholarly article
title: Polynomial filtrations and Lannes' \(T\)-functor
zbMATH Open document ID: 0892.55009
DOI: 10.1023/A:1007737116738
author: Geoffrey Powell
published in: \(K\)-Theory
publication date: 1998-07-21T00:00:00Z
review text: The author's abstract. ``This paper defines and studies the polynomial filtration \([p_k \widetilde \Delta]\) of the shift functor \(\widetilde \Delta: {\mathcal F} \to {\mathcal F}\), where \({\mathcal F}\) is the category of functors between \(\mathbb{F}\)-vector spaces over a finite field \(\mathbb{F}\). The functors \([p_k \widetilde \Delta]\) correspond to a system of functors \((p_kT): {\mathcal U} \to {\mathcal U}\), related to Lannes' \(T\)-functor on the category \({\mathcal U}\) of unstable modules over the Steenrod algebra. The main results concern the behaviour of the quotients \(\widetilde \nabla_s: =\widetilde \Delta/[p_{s-1} \widetilde \Delta]\); filtrations by \(\widetilde \nabla_s\)-nilpotent functors are introduced and it is shown that the full subcategory of \(\widetilde \nabla_s\)-nilpotent functors is thick.
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 18G05
zbMATH DE Number: 1139540
zbMATH Keywords: functors
zbMATH Keywords: polynomial functor
zbMATH Keywords: Steenrod algebra
reviewed by: Saïd Zarati
MaRDI profile type: Publication
full work available at URL: a:1007737116738
OpenAlex ID: W2070633665
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description: scientific article; zbMATH DE number 1139540