From triangulated categories to abelian categories: cluster tilting in a general framework |
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| Authors: | Steffen Koenig Bin Zhu |
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| Affiliation: | 1.Mathematisches Institut,Universit?t zu K?ln,K?ln,Germany;2.Department of Mathematical Sciences,Tsinghua University,Beijing,People’s Republic of China |
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| Abstract: | 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. |
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| Keywords: | Triangulated categories Abelian categories 1-Orthogonal categories Tilting Cluster categories Gorenstein algebras |
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