Type: Article

Noetherianity and Gelfand-Kirillov dimension of components

Roberto Martínez-Villa; Oyvind Solberg;

Abstract:

The category of all additive functors Mod(mod A) for a finite dimensional algebra A were shown to be left Noetherian if and only if A is of finite representation type by M. Auslander. Here we consider the category of all additive graded functors from the category of associated graded category of mod A to graded vector spaces. This category decomposes into subcategories corresponding to the components of the Auslander-Reiten quiver. For a regular component we show that the corresponding graded functor category is left Noetherian if and only if the section of the component is extended Dynkin or infinite Dynkin.