Representations of Algebras and Related Topics

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pp: 251–353

DOI: 10.4171/101-1/7

Algebras with separating Auslander–Reiten components

Piotr Malicki[1] and Andrzej Skowroński[2]

(1) Nicolaus Copernicus University, Torun, Poland
(2) Nicolaus Copernicus University, Torun, Poland

We survey old and new results on the structure and homological properties of Artin algebras whose Auslander–Reiten quiver admits a separating family of connected components.

Keywords: Artin algebra, Gabriel quiver, module category, tilting module, Auslander–Reiten quiver, Auslander–Reiten component, separating family of Auslander–Reiten components, heart of a module category, component quiver, generalized standard component, tube, ray tube, coray tube, generalized multicoil, hereditary algebra, tilted algebra, tubular algebra, quasitilted algebra, double tilted algebra, generalized double tilted algebra, generalized multicoil algebra, tame algebra, generic module