Classifying orders in the Sklyanin algebra

Let S denote the 3-dimensional Sklyanin algebra over an algebraically closed field k and assume that S is not a finite module over its centre. (This algebra corresponds to a generic noncommutative P-2.) Let A = circle plus(i >= 0) A(i) be any connected graded k-algebra that is contained in and has the same quotient ring as a Veronese ring S-(3n). Then we give a reasonably complete description of the structure of A. This is most satisfactory when A is a maximal order, in which case we prove, subject to a minor technical condition, that A is a noncommutative blowup of S-(3n) at a (possibly noneffective) divisor on the associated elliptic curve E. It follows that A has surprisingly pleasant properties; for example, it is automatically noetherian, indeed strongly noetherian, and has a dualising complex.