Graded modules of Gelfand-Kirillov dimension one over three-dimensional Artin-Schelter regular algebras

Abstract

Let A be a three dimensional Artin-Schelter regular algebra. We give a description of the category of finitely generated A-modules of Gelfand-Kirillov dimension one (module those of finite dimension over the ground field). The proof is based upon a result by Gabriel which says that locally finite categories can be described by module categories over topological rings.