Crossed Products of Semisimple Cocommutative Hopf Algebras
Crossed Products of Semisimple Cocommutative Hopf Algebras
We provide a short proof of an analog of Nagataâs theorem for finite-dimensional Hopf algebras. The result, proved Hopf-algebraically by Sweedler and using group schemes by Demazure and Gabriel, says that a finite-dimensional cocommutative semisimple irreducible Hopf algebra is commutative. With mild base field assumptions such a Hopf algebra is …