Normalizing extensions of the two-Veronese of a three dimensional Artin-Schelter regular algebra on two generators (Q1270375)

The aim of the paper is to study Koszul algebras \(D\) that have a normalizing element \(C\) of degree two, such that the quotient \(D/(C)\) is the two-Veronese of a three-dimensional regular algebra \(A\) on two generators. Such an algebra \(D\) is Auslander regular of global dimension 4 and Cohen-Macaulay with respect to GK-dimension. Some classification results are given and it is shown that among these algebras one finds the four-dimensional Sklyanin algebras. The point-variety is studied and new classes of four-dimensional regular algebras are found.