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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-3,
author = {K. Erdmann and D. Madsen and V. Miemietz},
title = {On Auslander-Reiten translates in functorially finite subcategories and applications},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {51-77},
zbl = {1220.16015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-3}
}
K. Erdmann; D. Madsen; V. Miemietz. On Auslander-Reiten translates in functorially finite subcategories and applications. Colloquium Mathematicae, Tome 120 (2010) pp. 51-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-3/