On Auslander-Reiten translates in functorially finite subcategories and applications

K. Erdmann, D. Madsen, and V. Miemietz. "On Auslander-Reiten translates in functorially finite subcategories and applications." Colloquium Mathematicae 119.1 (2010): 51-77. <http://eudml.org/doc/284240>.

@article{K2010,
abstract = {We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when this category has finite type. The class of these algebras contains all blocks of Schur algebras S(2,r).},
author = {K. Erdmann, D. Madsen, V. Miemietz},
journal = {Colloquium Mathematicae},
keywords = {Artin algebras; categories of finitely generated modules; Auslander-Reiten sequences; cotilting modules; bounded derived categories; quasi-hereditary algebras; Schur algebras},
language = {eng},
number = {1},
pages = {51-77},
title = {On Auslander-Reiten translates in functorially finite subcategories and applications},
url = {http://eudml.org/doc/284240},
volume = {119},
year = {2010},
}

TY - JOUR
AU - K. Erdmann
AU - D. Madsen
AU - V. Miemietz
TI - On Auslander-Reiten translates in functorially finite subcategories and applications
JO - Colloquium Mathematicae
PY - 2010
VL - 119
IS - 1
SP - 51
EP - 77
AB - We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when this category has finite type. The class of these algebras contains all blocks of Schur algebras S(2,r).
LA - eng
KW - Artin algebras; categories of finitely generated modules; Auslander-Reiten sequences; cotilting modules; bounded derived categories; quasi-hereditary algebras; Schur algebras
UR - http://eudml.org/doc/284240
ER -