Covering theory for linear categories with application to derived categories

DOI10.1016/j.jalgebra.2014.02.016zbMath1331.18013OpenAlexW2034715297MaRDI QIDQ402433

Shiping Liu, Raymundo Bautista

Publication date: 28 August 2014

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2014.02.016

zbMATH Keywords

almost split sequencesirreducible morphismsAuslander-Reiten quiver of a Krull-Schmidt categoryderived categories of abelian categoriesGalois covering of categoriesGalois covering of quiversmodules over a locally bounded linear category

Mathematics Subject Classification ID

Related Items (17)

Unfolding of sign-skew-symmetric cluster algebras and its applications to positivity and \(F\)-polynomials ⋮ Minimal model of Ginzburg algebras ⋮ ON HIGHER TORSION CLASSES ⋮ On a family of Caldero-Chapoton algebras that have the Laurent phenomenon ⋮ Gorenstein versions of covering techniques for linear categories and their applications ⋮ Almost split sequences in tri-exact categories ⋮ Morphisms determined by objects under Galois \(G\)-covering theory ⋮ The Auslander-Reiten quiver of the category of \(m\)-periodic complexes ⋮ Galois covering of pure-semisimple categories ⋮ Group actions on cluster algebras and cluster categories ⋮ The derived category of an algebra with radical square zero ⋮ The bounded derived categories of an algebra with radical squared zero ⋮ Cluster categories of type \({\mathbb {A}}_\infty ^\infty \) and triangulations of the infinite strip ⋮ \(d\)-representation-finite self-injective algebras ⋮ Cyclic complexes, Hall polynomials and simple Lie algebras. ⋮ Lie algebras arising from 1-cyclic perfect complexes ⋮ Galois \(G\)-covering of quotients of linear categories

Cites Work

• Auslander-Reiten theory in a Krull-Schmidt category
• A generalization of Gabriel's Galois covering functors and derived equivalences
• Tame algebras and integral quadratic forms
• Algebren, Darstellungsköcher, Überlagerungen und zurück
• Covering spaces in representation-theory
• A covering technique for derived equivalence
• Tilting theory and cluster combinatorics.
• Localization theory for triangulated categories
• Graphs with Relations, Coverings and Group-Graded Algebras
• Representation theory of artin algebras IV¹⁾Invariants given by almost split sequences
• Idempotent completion of triangulated categories
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