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.