An embedding for the \(E_{2}\)-term of the Adams spectral sequence at odd primes
type: Item
instance of: scholarly article
title: An embedding for the \(E_{2}\)-term of the Adams spectral sequence at odd primes
zbMATH Open document ID: 1118.55011
author: Maurizio Brunetti
author: A. Ciampella
author: Luciano Amito Lomonaco
publication date: 2007-05-24T00:00:00Z
review text: In an earlier paper [Ricerche Mat., to appear] the first and third author studied an algebra homomorphism \(\overline{\pi}:Q_1 \to {\mathcal A}\), where \({\mathcal A}\) denotes the mod \(2\) Steenrod algebra, and showed that the induced homomorphism \(\text{Ext}_{\mathcal A}({\mathbb F}_2,{\mathbb F}_2) \to \text{Ext}_{Q_1}({\mathbb F}_2,{\mathbb F}_2)\) was injective. Hence the \(E_2\)-term of the Adams spectral sequence is displayed as a subalgebra of this latter Ext group. The algebra \(Q_1\) is related to the algebra \(Q\) of cohomology operations in the category of \(H_{\infty}\)-ring spectra, as studied by \textit{J. P. May} [Steenrod Algebra Appl., Lect. Notes Math. 168, 153--231 (1970; Zbl 0242.55023)], by a change of Koszul generators. In the paper under review the authors carry out the analogous programme for odd primes. They also offer a more specific relation between the two Ext groups under the assumption that \(Q\) is Koszul. It is not yet clear that this assumption holds but the authors offer some evidence for it.
reviewed by: Martin D. Crossley
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 55T15
zbMATH DE Number: 5156860
zbMATH Keywords: Koszul algebras
zbMATH Keywords: cohomology of algebras
zbMATH Keywords: Adams spectral sequence
zbMATH Keywords: Steenrod algebra
MaRDI profile type: Publication
full work available at URL: s10114-005-0704-4
OpenAlex ID: W2027182506
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DOI: 10.1007/S10114-005-0704-4
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5156860