The structure and homological properties of generalized standard Auslander-Reiten components

JOURNAL OF ALGEBRA

卷:518

Article

Malicki, Piotr¹  Skowronski, Andrzej¹ 

[1] Nicolaus Copernicus Univ, Fac Math & Comp Sci, Chopina 12-18, PL-87100 Torun, Poland

关键词: Artin algebra;    Auslander-Reiten quiver;    Generalized standard component;    Tilted algebra;    Quasitilted algebra;    Euler form;    Generically tame algebra;   

DOI  :  10.1016/j.jalgebra.2018.10.015

来源: Elsevier

【 摘 要 】

We describe the structure and homological properties of arbitrary generalized standard Auslander Reiten components of artin algebras. In particular, we prove that for all but finitely many indecomposable modules in such components the Euler characteristic is defined and nonnegative. Further, we provide a handy criterion for an infinite Auslander Reiten component of an artin algebra to be generalized standard. We solve also the long standing open problem concerning the structure of artin algebras admitting a separating family of Auslander Reiten components. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free