Examples of Non-Semisimple Hopf Algebra Actions on Artin-Schelter Regular Algebras

Let 𝕜\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Bbbk $\end{document} be a base field of characteristic p > 0 and let U be the restricted enveloping algebra of a 2-dimensional nonabelian restricted Lie algebra. We classify all inner-faithful U-actions on noetherian Koszul Artin-Schelter regular algebras of global dimension up to three.