A translation principle for Sklyanin algebras

Abstract

In this paper we prove a translation principle for the central quotients of four-dimensional Sklyanin algebras, which is analogous to the translation principle for semi-simple Lie algebras. In the course of the proof we construct an “elliptic” analog of the sheaf of differential operators on21. The translation principle may be used to construct the fat points of a four-dimensional, non-PI, Sklyanin algebra.