Homotopy theory of simplicial abelian Hopf algebras Original Research Article

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.