\(\tau\)-tilting theory and \(*\)-modules.

DOI10.1016/j.jalgebra.2014.04.028zbMath1330.16005OpenAlexW1998172691MaRDI QIDQ740234

Jiaqun Wei

Publication date: 2 September 2014

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2014.04.028

zbMATH Keywords

triangulated categoriestorsion classesArtin algebrasmutationscluster-tilting objects\(\tau\)-tilting modulesquasi-tilting modulessilting complexes

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Representations of associative Artinian rings (16G10) Syzygies, resolutions, complexes in associative algebras (16E05)

Related Items

\(G\)-stable support \(\tau\)-tilting modules ⋮ Classifying tilting modules over the Auslander algebras of radical square zero Nakayama algebras ⋮ Tilting modules over Auslander-Gorenstein algebras ⋮ \(\tau\)-rigid modules over Auslander algebras ⋮ Classifying \(\tau\)-tilting modules over the Auslander algebra of \(K[x/(x^n)\)] ⋮ Three results for \(\tau\)-rigid modules ⋮ Quasi-cotilting modules and torsion-free classes ⋮ On mutation of τ-tilting modules

Cites Work

• Representable equivalences between categories of modules and applications
• Representable equivalences are represented by tilting modules
• Addendum to ``Almost split sequences in subcategories
• On the structure of *-modules
• Every *-module is finitely generated
• Quasi-tilting modules and counter equivalences
• Some remarks on equivalences between categories of modules
• Tilting modules and ∗-modules
• Tilting and torsion theory counter equivalences
• -tilting theory

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