\(\tau\)-categories. II: Nakayama pairs and rejective subcategories.

DOI10.1007/s10468-005-0969-4zbMath1124.16017OpenAlexW2082954273MaRDI QIDQ2644165

Osamu Iyama

Publication date: 7 September 2007

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10468-005-0969-4

zbMATH Keywords

Auslander-Reiten quivershammocksindecomposable latticesladdersgeneralized overordersNakayama pairsAuslander-Reiten squaresorderlike \(\tau\)-categoriesrejective subcategories

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Module categories in associative algebras (16D90) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Preadditive, additive categories (18E05)

Related Items (21)

Finiteness of representation dimension ⋮ Computing global dimension of endomorphism rings via ladders ⋮ The relationship between homological properties and representation theoretic realization of artin algebras ⋮ Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories. ⋮ Exact categories, big Cohen-Macaulay modules and finite representation type ⋮ Characterizations of right rejective chains ⋮ Artin-Schelter regular algebras and categories. ⋮ Auslander–Reiten theory in extriangulated categories ⋮ Symmetry and duality on \(n\)-Gorenstein rings. ⋮ On an upper bound for the global dimension of Auslander-Dlab-Ringel algebras ⋮ The classification of special Cohen-Macaulay modules ⋮ \(\tau\)-categories. I: Ladders. ⋮ The category of lattices over a lattice-finite ring. ⋮ Lattice-finite rings. ⋮ Triadic categories without localization ⋮ Wild algebras have one-point extensions of representation dimension at least four. ⋮ Exact Krull-Schmidt categories with finitely many indecomposables ⋮ On the abundance of silting modules ⋮ Non-commutative resolutions and Grothendieck groups ⋮ \(\tau\)-categories. III: Auslander orders and Auslander-Reiten quivers. ⋮ Regular over-orders of lattice-finite rings and the Krull-Schmidt property.

Cites Work

• \(\tau\)-categories. III: Auslander orders and Auslander-Reiten quivers.
• A generalization of rejection lemma of Drozd-Kirichenko
• Bass orders in non semisimple algebras
• \(\tau\)-categories. I: Ladders.
• Lattices over orders. II
• Classification of Bass orders.
• Stable module theory

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