Homotopy theory of simplicial abelian Hopf algebras

Paul Goerss*, James Turner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We examine the homotopy theory of simplicial graded abelian Hopf algebras over a prime field Fp, p>0, proving that two very different notions of weak equivalence yield the same homotopy category. We then prove a splitting result for the Postnikov tower of such simplicial Hopf algebras. As an application, we show how to recover the homotopy groups of a simplicial Hopf algebra from its André-Quillen homology, which, in turn, can be easily computed from the homotopy groups of the associated simplicial Dieudonné module.

Original languageEnglish (US)
Pages (from-to)167-206
Number of pages40
JournalJournal of Pure and Applied Algebra
Volume135
Issue number2
DOIs
StatePublished - Feb 15 1999

ASJC Scopus subject areas

  • Algebra and Number Theory

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