The irreducible representations of 3-dimensional Sklyanin algebras

TL;DR

This paper provides a comprehensive classification of simple representations of 3-dimensional Sklyanin algebras linked to torsion points, utilizing classical representation theory of graded rings.

Contribution

It offers the first complete description of irreducible representations of these specific Sklyanin algebras, connecting them to classical results.

Findings

Complete classification of simple representations for the algebra

Connection established between Sklyanin algebras and classical graded ring theory

Enhanced understanding of the algebra's representation theory

Abstract

In this article a complete description is given of the simple representations of a 3-dimensional Sklyanin algebra associated to a torsion point. In order to determine these irreducible representations, a review is given of classical results regarding representation theory of graded rings with excellent homological and algebraic properties.