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arXiv · 1802.02773

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

Piotr Malicki·Andrzej Skowroński
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Abstract

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.

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BibTeXRIS

Piotr Malicki, Andrzej Skowroński. 2018-02-08. The structure and homological properties of generalized standard Auslander-Reiten components. https://arxiv.org/abs/1802.02773

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