Frobenius algebras. II: Tilted and Hochschild extension algebras

DOI10.4171/174zbMath1378.16001OpenAlexW2758345502MaRDI QIDQ2627220

Andrzej Skowroński, Yamagata, Kunio

Publication date: 30 May 2017

Published in: EMS Textbooks in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/174

zbMATH Keywords

representationcategoryidealprojective moduleglobal dimensionassociative algebraGrothendieck groupfunctorsimple modulemodulequiverAuslander-Reiten quiversymmetric algebracomposition seriesbimoduleuniserial moduleprojective functorFrobenius algebraalmost split sequencestable categoryNakayama automorphismEuler formindecomposable moduleinjective modulehereditary algebratilting moduletorsion pairDynkin quiverEuclidean quiverGabriel quiverAuslander-Reiten translationself-injective algebrastable equivalenceirreducible homomorphismtilted algebraNakayama functorstable modulesubfunctorsyzygy functortrivial extension algebrastable tubesimple functorbound quiver algebraHochschild extension algebraself-duality bimodule

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Injective modules, self-injective associative rings (16D50) Module categories in associative algebras (16D90) (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) 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) Representations of associative Artinian rings (16G10) Quadratic and bilinear forms, inner products (15A63) Multilinear algebra, tensor calculus (15A69) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Homological dimension in associative algebras (16E10) Functor categories, comma categories (18A25) Extensions of associative rings by ideals (16S70) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras (16-01) Modules, bimodules and ideals in associative algebras (16D99)

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