A translation principle for the four-dimensional 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 on P-1. The translation principle may be used to construct the fat points of a four-dimensional, non-PI, Sklyanin algebra. (C) 1996 Academic Press, Inc.