The Global Dimension of the Endomorphism Algebra of a Generator-cogenerator for a Subcategory

DOI10.1142/S1005386713000424zbMath1304.16008MaRDI QIDQ2854032

Jing-Jing Guo

Publication date: 17 October 2013

Published in: Algebra Colloquium (Search for Journal in Brave)

zbMATH Keywords

tilting modulesgeneratorsglobal dimensionAuslander-Reiten quiverscategories of finitely generated modulescogeneratorshereditary Artin algebrasrelative AR-sequences

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Module categories in associative algebras (16D90) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) 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) Homological dimension in associative algebras (16E10)

Cites Work

• Existence of Auslander-Reiten sequences in subcategories.
• Auslander-Reiten sequences and global dimensions.
• Almost split sequences in subcategories
• The connected components of the Auslander-Reiten quiver of a tilted algebra
• Approximations and almost split sequences in homologically finite subcategories
• Applications of contravariantly finite subcategories
• The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences

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