Polynomial Identities in Hopf Algebras: Passman’s Theorem and Its Dual

Abstract

We give necessary and sufficient conditions when a cocommutative Hopf algebra of characteristic 0 satisfies an identity as an algebra, which can be considered as a generalization of Passman’s theorem on group algebras. Then we look at the dual situation: when a commutative Hopf algebra (not necessarily of characteristic 0) satisfies an identity as a coalgebra.