TY - JOUR

T1 - Homotopy theory of simplicial abelian Hopf algebras

AU - Goerss, Paul

AU - Turner, James

N1 - Funding Information:
* Corresponding author. E-mail: pgoerss@math.washington.edu. Supported by the National Science Foundation. ’ Current address: Department of Mathematics, College of the Holy Cross, Worcester, MA 01610, USA.

PY - 1999/2/15

Y1 - 1999/2/15

N2 - 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.

AB - 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.

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U2 - 10.1016/S0022-4049(97)00142-4

DO - 10.1016/S0022-4049(97)00142-4

M3 - Article

AN - SCOPUS:0033556967

VL - 135

SP - 167

EP - 206

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 2

ER -