A Note on the Algebra of Operations for Hopf Cohomology at Odd Primes

Abstract

Let $p$ be any prime, and let $\mathcal{B}(p)$ be the algebra of operations on the cohomology ring of any cocommutative ${\mathbb{F}}_p$-Hopf algebra. In this paper we show that when $p$ is odd (and unlike the $p=2$ case), $\mathcal{B}(p)$ cannot become an object in the Singer category of ${\mathbb{F}}_p$-algebras with coproducts, if we require that coproducts act on the generators of $\mathcal{B}(p)$ coherently with their nature of cohomology operations