Bicommutativity for a class of graded connected Hopf algebras
The authors show that if \(A\) is a graded connected Hopf algebra over a field of characteristic \(0\) such that all homogeneous elements of strictly positive degree are nilpotent, then \(A\) is commutative and cocommutative. Hence \(A\) is an exterior algebra over the primitive elements. As a consequence, any finite-dimensional graded connected Hopf algebra is commutative and cocommutative. This recovers a result of \textit{H. Hopf} [in Ann. Math., II. Ser. 42, 33-52 (1941; Zbl 0025.09303)].
finite-dimensional graded connected Hopf algebras
scientific article; zbMATH DE number 1308302