Trisections of module categories

José A. de la Peña; Idun Reiten

Colloquium Mathematicae (2007)

  • Volume: 107, Issue: 2, page 191-219
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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José A. de la Peña, and Idun Reiten. "Trisections of module categories." Colloquium Mathematicae 107.2 (2007): 191-219. <http://eudml.org/doc/284306>.

@article{JoséA2007,
abstract = {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.},
author = {José A. de la Peña, Idun Reiten},
journal = {Colloquium Mathematicae},
keywords = {trisections of module categories; Auslander-Reiten quivers; standard components; factorization properties; finite-dimensional algebras; decompositions of categories of finitely generated modules},
language = {eng},
number = {2},
pages = {191-219},
title = {Trisections of module categories},
url = {http://eudml.org/doc/284306},
volume = {107},
year = {2007},
}

TY - JOUR
AU - José A. de la Peña
AU - Idun Reiten
TI - Trisections of module categories
JO - Colloquium Mathematicae
PY - 2007
VL - 107
IS - 2
SP - 191
EP - 219
AB - 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.
LA - eng
KW - trisections of module categories; Auslander-Reiten quivers; standard components; factorization properties; finite-dimensional algebras; decompositions of categories of finitely generated modules
UR - http://eudml.org/doc/284306
ER -

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