Geodesic
Trisections of module categories
José A. de la Peña 1   ; Idun Reiten 2
1 Instituto de Matemáticas UNAM Circuito Exterior Ciudad Universitaria México 04510, D.F., México
2 Institutt for Matematikk og Statistikk Universitetet i Trondheim, AVH N-7055 Dragvoll, Norway
Colloquium Mathematicum, Tome 107 (2007) no. 2, pp. 191-219 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

Let $A$ be a finite-dimensional algebra over a field $k$. We discuss the existence of trisections $(\mathop{\rm mod}\nolimits_+A,\mathop{\rm mod}\nolimits_0A,\mathop{\rm mod}\nolimits_-A)$ 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 $\mathop{\rm mod}\nolimits_0A$.
DOI : 10.4064/cm107-2-3
Keywords: finite dimensional algebra field discuss existence trisections mathop mod nolimits mathop mod nolimits mathop mod nolimits a category finitely generated modules mod satisfying exactness standardness separation adjustment conditions many important classes algebras admit trisections describe construction algebras admitting trisection their module categories special cases describe structure components auslander reiten quiver lying mathop mod nolimits

José A. de la Peña  1   ; Idun Reiten  2

1 Instituto de Matemáticas UNAM Circuito Exterior Ciudad Universitaria México 04510, D.F., México
2 Institutt for Matematikk og Statistikk Universitetet i Trondheim, AVH N-7055 Dragvoll, Norway 
@article{10_4064_cm107_2_3,
     author = {Jos\'e A. de la Pe\~na and Idun Reiten},
     title = {Trisections of module categories},
     journal = {Colloquium Mathematicum},
     pages = {191--219},
     year = {2007},
     volume = {107},
     number = {2},
     doi = {10.4064/cm107-2-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm107-2-3/}
}
TY  - JOUR
AU  - José A. de la Peña
AU  - Idun Reiten
TI  - Trisections of module categories
JO  - Colloquium Mathematicum
PY  - 2007
SP  - 191
EP  - 219
VL  - 107
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm107-2-3/
DO  - 10.4064/cm107-2-3
LA  - en
ID  - 10_4064_cm107_2_3
ER  - 
%0 Journal Article
%A José A. de la Peña
%A Idun Reiten
%T Trisections of module categories
%J Colloquium Mathematicum
%D 2007
%P 191-219
%V 107
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/cm107-2-3/
%R 10.4064/cm107-2-3
%G en
%F 10_4064_cm107_2_3
José A. de la Peña; Idun Reiten. Trisections of module categories. Colloquium Mathematicum, Tome 107 (2007) no. 2, pp. 191-219. doi: 10.4064/cm107-2-3

Cité par Sources :