Geodesic
On Auslander–Reiten translates in functorially finite subcategories and applications
K. Erdmann 1   ; D. Madsen 2   ; V. Miemietz 1
1 Mathematical Institute University of Oxford 24-29 St Giles' OX1 3LB, Oxford, UK
2 Mathematics Department 215 Carnegie Syracuse University Syracuse, NY 13244, U.S.A.
Colloquium Mathematicum, Tome 119 (2010) no. 1, pp. 51-77 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $S(2,r)$.
DOI : 10.4064/cm119-1-3
Keywords: consider functorially finite subcategories module categories artin algebras main result provides method setup bounded derived categories compute approximations end terms relative auslander reiten sequences prove auslander reiten formula setting functorially finite subcategories furthermore study category modules filtered standard modules certain quasi hereditary algebras classify precisely category has finite type class these algebras contains blocks schur algebras

K. Erdmann  1   ; D. Madsen  2   ; V. Miemietz  1

1 Mathematical Institute University of Oxford 24-29 St Giles' OX1 3LB, Oxford, UK
2 Mathematics Department 215 Carnegie Syracuse University Syracuse, NY 13244, U.S.A. 
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K. Erdmann; D. Madsen; V. Miemietz. On Auslander–Reiten translates in functorially finite subcategories and applications. Colloquium Mathematicum, Tome 119 (2010) no. 1, pp. 51-77. doi: 10.4064/cm119-1-3

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