The irreducible representations of 3-dimensional Sklyanin algebras

2017/07/12 by Kevin De Laet, De Laet, Kevin
Mathematics · #16G99 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1707.03813

openalex publication_date 2017/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A formal inverse to the Cayley-Hamilton theorem
• The superpotential XYZ+XZY+(c)/(3)(X³+Y³+Z³)

Related

• Blowup subalgebras of the Sklyanin algebra
• Character series and Sklyanin algebras at points of order 2
• Homological properties of 3-dimensional DG Sklyanin algebras
• Ideal classes of three dimensional Sklyanin algebras
• Quotients of degenerate Sklyanin algebras