From subcategories to the entire module categories

Rasool Hafezi

Published 2019-05-21Version 1

In this paper we show that how the representation theory of subcategories (of the module category over an Artin algebra) can be connected to the representation theory of all module over some algebra. The subcategories dealing with are some certain subcategories of the morphism category (including submodule categories) and the Gorenstein projective modules over (relative) stable Auslander algebras. These two kinds of subcategories, as will be seen, are closely related to each other. It is shown that to compute the almost split sequences in the subcategories it is enough to do the computation in the module category of some algebra which is known and easier to work. Then as an application the most part of Auslander-Reiten quiver of the subcategories is obtained only by the Ausalander-Reiten quiver of an appropriate algebra and next adding the remaining vertices and arrows in an obvious way.