  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.

Rings and Algebras;Quantum Algebra