Let A be a finite-dimensional algebra over a field k. We discuss the existence of trisections (mod₊ A,mod₀ A,mod₋ A) of the category of finitely generated modules mod A satisfying exactness, standardness, separation and adjustment conditions. Many important classes of algebras admit trisections. We describe a construction of algebras admitting a trisection of their module categories and, in special cases, we describe the structure of the components of the Auslander-Reiten quiver lying in mod₀ A.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-3,
author = {Jos\'e A. de la Pe\~na and Idun Reiten},
title = {Trisections of module categories},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {191-219},
zbl = {1169.16006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-3}
}
José A. de la Peña; Idun Reiten. Trisections of module categories. Colloquium Mathematicae, Tome 107 (2007) pp. 191-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-3/