Higher conjugation cohomology in commutative hopf algebras

Abstract

Let A be a graded, commutative Hopf algebra. We study an action of the symmetric group Sn on the tensor product of n −1 copies of A; this action was introduced by the second author in [8] and is relevant to the study of commutativity conditions on ring spectra in stable homotopy theory [6]. We show that for a certain class of Hopf algebras the cohomology ring //(En ; /1∼l) is independent of the coproduct provided n and (n −2)! are invertible in the ground ring. With the simplest coproduct structure, the group action becomes particularly tractable and we discuss the implications this has for computations. © 2001 Edinburgh Mathematical Society.