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