REGULARITY CRITERION AND CLASSIFICATION FOR ALGEBRAS OF JORDAN TYPE

We show that Artin-Schelter regularity of a Z-graded algebra can be examined by its associated Z(r)-graded algebra. We prove that there is exactly one class of four-dimensional Artin-Schelter regular algebras with two generators of degree one in the Jordan type. This class is strongly noetherian, Auslander regular, and Cohen-Macaulay. Their automorphisms and point modules are described.