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∞-Ext-algebras