Zariski cancellation problem for noncommutative algebras

A noncommutative analogue of the Zariski cancellation problem asks whether A[x]≅B[x]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A[x]\cong B[x]$$\end{document} implies A≅B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\cong B$$\end{document} when A and B are noncommutative algebras. We resolve this affirmatively in the case when A is a noncommutative finitely generated domain over the complex field of Gelfand–Kirillov dimension two. In addition, we resolve the Zariski cancellation problem for several classes of Artin–Schelter regular algebras of higher Gelfand–Kirillov dimension.