HIGHER CONJUGATION COHOMOLOGY IN COMMUTATIVE HOPF ALGEBRAS

M. D. Crossley, Sarah Whitehouse
2001 Proceedings of the Edinburgh Mathematical Society  
Let A be a graded, commutative Hopf algebra. We study an action of the symmetric group Σ n 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 H * (Σ n ; A ⊗n−1 ) is independent of the coproduct provided n and (n − 2)! are invertible in the ground ring. Then, by choosing a
more » ... , by choosing a sufficiently simple coproduct, we are able to deduce significant information about the Σ n invariants of A ⊗n−1 , including dimensions and algebra structure.
doi:10.1017/s0013091599000826 fatcat:hrblpxgmq5ba3mj3sgw5qgurgy