From triangulated categories to abelian categories: cluster tilting in a general framework

From triangulated categories to abelian categories: cluster tilting in a general framework

A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (i.e., a maximal 1-orthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of d...

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Veröffentlicht in:Mathematische Zeitschrift 2008-01, Vol.258 (1), p.143-160
Hauptverfasser: Koenig, Steffen, Zhu, Bin
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (i.e., a maximal 1-orthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-007-0165-9