Homotopy and homology of simplicial Abelian Hopf algebras
type: Item
instance of: scholarly article
title: Homotopy and homology of simplicial Abelian Hopf algebras
zbMATH Open document ID: 0940.16006
DOI: 10.1007/PL00004702
author: Paul Goerss
author: James M. Turner
published in: Mathematische Zeitschrift
publication date: 2000-05-08T00:00:00Z
review text: This paper takes as its starting point the fact that the mod \(p\) cohomology of the Eilenberg-MacLane space \(K(G,n)\) (\(G\) Abelian and \(n>0\)) depends only on \(\text{Tor}_0(\mathbb{Z}/p,G)\) and \(\text{Tor}_1(\mathbb{Z}/p,G)\). The authors generalize this and emphasize that it is essentially an algebraic, not a topological, fact. The main result is that the homotopy of a connected, simplicial, bicommutative Hopf algebra over \(\mathbb{F}_2\) is a functor of its André-Quillen homology. Since the traditional approach to computing this homology uses the homotopy as input, the authors give a new method for this computation, using Dieudonné theory.
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 57T05
Mathematics Subject Classification ID: 18G55
Mathematics Subject Classification ID: 55P65
Mathematics Subject Classification ID: 55Q99
Mathematics Subject Classification ID: 55U35
zbMATH DE Number: 1295397
zbMATH Keywords: André-Quillen homology
zbMATH Keywords: Hopf algebras
zbMATH Keywords: Dieudonné theory
zbMATH Keywords: homotopy
reviewed by: Martin D. Crossley
MaRDI profile type: Publication
full work available at URL: pl00004702
OpenAlex ID: W2013336827
description: scientific article; zbMATH DE number 1295397