Graded Modules of Gelfand–Kirillov Dimension One over Three-Dimensional Artin–Schelter Regular Algebras

AbstractLetAbe a three dimensional Artin–Schelter regular algebra. We give a description of the category of finitely generatedA-modules of Gelfand–Kirillov dimension one (modulo 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