Cohomology of finite-dimensional connected cocommutative Hopf algebras
type: Item
instance of: scholarly article
title: Cohomology of finite-dimensional connected cocommutative Hopf algebras
zbMATH Open document ID: 0823.55014
DOI: 10.1016/0022-4049(94)90027-2
author: A. Bajer
author: Hal Sadofsky
published in: Journal of Pure and Applied Algebra
publication date: 1994-08-07T00:00:00Z
review text: Let \(A\) be a finite-dimensional cocommutative graded connected Hopf algebra. The May spectral sequence is obtained by filtering the bar construction for \(A\) by the filtration induced by filtering \(A\) by powers of its augmentation ideal. The authors give a sufficient condition for the existence of some finite \(r\) such that \(E_ r = E_ \infty\). As a corollary they show that the May spectral sequence stops at a finite state for the subalgebras of the Steenrod algebra \(A(n)\) for \(p = 2\) and \(P(n)\) for \(p > 2\). They also consider the Ivanovskij spectral sequence obtained by filtering the cobar construction on \(A\) by copowers of the unit co-ideal. They show that this spectral sequence stops at \(E_ r\) for some finite \(r\).
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 55T99
Mathematics Subject Classification ID: 57T30
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 57T05
zbMATH DE Number: 612141
zbMATH Keywords: finite-dimensional cocommutative graded connected Hopf algebra
zbMATH Keywords: May spectral sequence
zbMATH Keywords: bar construction
zbMATH Keywords: subalgebras of the Steenrod algebra
zbMATH Keywords: Ivanovskij spectral sequence
zbMATH Keywords: cobar construction
reviewed by: Yves Félix
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90027-2
OpenAlex ID: W2079058443
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Wikidata QID: Q128028717
description: scientific article; zbMATH DE number 612141