$n$-representation-finite algebras and $n$-APR tilting

DOI10.1090/S0002-9947-2011-05312-2zbMath1264.16015arXiv0909.0593OpenAlexW2963269325MaRDI QIDQ3103857

Publication date: 12 December 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.0593

zbMATH Keywords

derived categories path algebras Auslander-Reiten theory preprojective algebras quivers with relations Auslander algebras cluster tilting modules $n$-representation-finite algebras $n$-representation-finiteness APR tilting modules representation-finite hereditary algebras

Mathematics Subject Classification ID

Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Derived categories and associative algebras (16E35)

Related Items (59)

Higher Auslander correspondence for dualizing $R$-varieties ⋮ $n$-exangulated categories (I): definitions and fundamental properties ⋮ $n\mathbb{Z}$-Gorenstein cluster tilting subcategories ⋮ ON HIGHER TORSION CLASSES ⋮ $n$-abelian and $n$-exact categories ⋮ Derived equivalences in $n$-angulated categories ⋮ Cluster tilting for tilted algebras. ⋮ Existence of n-Auslander–Reiten sequences via a finiteness condition ⋮ Representation theory of quivers and finite dimensional algebras. Abstracts from the workshop held February 16--22, 2014. ⋮ $n$-cluster tilting subcategories for radical square zero algebras ⋮ New interpretations of the higher Stasheff-Tamari orders ⋮ The role of gentle algebras in higher homological algebra ⋮ On faithfully balanced modules, F-cotilting and F-Auslander algebras ⋮ Cluster tilting for higher Auslander algebras. ⋮ Quotients of exact categories by cluster tilting subcategories as module categories ⋮ Higher zigzag algebras ⋮ Representation Theory of Geigle-Lenzing Complete Intersections ⋮ Serre functors and graded categories ⋮ Representation theory of quivers and finite-dimensional algebras. Abstracts from the workshop held February 12--18, 2023 ⋮ Quiver combinatorics and triangulations of cyclic polytopes ⋮ Higher APR tilting preserves $n$-representation infiniteness ⋮ Auslander-Gorenstein algebras and precluster tilting ⋮ The Nakayama automorphism of a self‐injective preprojective algebra ⋮ Quasi-hereditary covers of higher zigzag algebras of type $A$ ⋮ Tensor products of higher almost split sequences in subcategories ⋮ ℤ Q type constructions in higher representation theory ⋮ Classification results for $n$-hereditary monomial algebras ⋮ A derived equivalence between cluster equivalent algebras. ⋮ Stable categories of higher preprojective algebras. ⋮ Realizing stable categories as derived categories ⋮ $n$-representation infinite algebras. ⋮ Classification of higher wide subcategories for higher Auslander algebras of type $A$ ⋮ $d \mathbb{Z}$-cluster tilting subcategories of singularity categories ⋮ Skew group algebras of Jacobian algebras ⋮ Tensor products of $n$-complete algebras ⋮ $n$-APR tilting and $\tau$-mutations ⋮ $d$-abelian quotients of $(d+2)$-angulated categories ⋮ Higher-dimensional cluster combinatorics and representation theory ⋮ $\tau^2$-stable tilting complexes over weighted projective lines ⋮ Higher Nakayama algebras. I: Construction ⋮ Constructing tilted algebras from cluster-tilted algebras. ⋮ Simplicial structures in higher Auslander-Reiten theory ⋮ Nakayama-type phenomena in higher Auslander–Reiten theory ⋮ $d$-representation-finite self-injective algebras ⋮ On $n$-translation algebras ⋮ Tropical friezes and the index in higher homological algebra ⋮ Gluing of $n$-cluster tilting subcategories for representation-directed algebras ⋮ Pure semisimple $n$-cluster tilting subcategories ⋮ d-Auslander–Reiten sequences in subcategories ⋮ The Grothendieck group of an $n$-exangulated category ⋮ Higher preprojective algebras, Koszul algebras, and superpotentials ⋮ On $n$-slice algebras and related algebras ⋮ Higher Auslander algebras of type 𝔸 and the higher Waldhausen 𝖲-constructions ⋮ Wide subcategories of 𝑑-cluster tilting subcategories ⋮ $n$-exangulated categories (II): constructions from $n$-cluster tilting subcategories ⋮ Selfinjective quivers with potential and 2-representation-finite algebras ⋮ THE COMBINATORICS OF TENSOR PRODUCTS OF HIGHER AUSLANDER ALGEBRAS OF TYPEA ⋮ The symplectic geometry of higher Auslander algebras: Symmetric products of disks ⋮ The existence of n-Auslander–Reiten sequences via determined morphisms

Cites Work

This page was built for publication: $n$-representation-finite algebras and $n$-APR tilting