Regular algebras of dimension 4 and their A-infinity Ext-algebras
  We construct four families of Artin-Schelter regular algebras of global dimension four. Under some generic conditions, this is a complete list of Artin-Schelter regular algebras of global dimension four that are generated by two elements of degree 1. These algebras are also strongly noetherian, Auslander regular and Cohen-Macaulay. One of the main tools is Keller's higher-multiplication theorem on A-infinity Ext-algebras. 
D.-M. Lu, J. H. Palmieri, Q.-S. Wu, J. J. Zhang