Regular algebras of dimension 4 and their A∞-Ext-algebras

Abstract

We construct four families of Artin-Schelter (AS) regular algebras of global dimension $4$. This is a complete list of AS regular algebras of global dimension $4$ which are generated by two elements of degree $1$ and whose Ext-algebra satisfies certain “generic” conditions. These algebras are also strongly Noetherian, Auslander regular, and Cohen-Macaulay. One of the main tools is Keller's higher-multiplication theorem on $A_{\infty }$-Ext-algebras