A Poincare-Birkhoff-Witt theorem for Hopf algebras with central Hopf algebra coradical

TL;DR

This paper proves that in characteristic zero, Hopf algebras with a central Hopf algebra coradical possess a Poincare-Birkhoff-Witt basis as modules over the coradical, extending classical PBW results.

Contribution

It establishes a PBW theorem for a class of Hopf algebras with central coradicals, broadening the understanding of their structure.

Findings

Existence of PBW basis for these Hopf algebras

Extension of classical PBW theorem to new algebra class

Structural insights into Hopf algebras with central coradicals

Abstract

We show that over fields of characteristic zero a Hopf algebra with central Hopf algebra coradical has a PBW basis as a module over the coradical.