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

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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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Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Köln, Germany

    Steffen Koenig

  2. Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, People’s Republic of China

    Bin Zhu

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  1. Steffen Koenig
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  2. Bin Zhu
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Correspondence to Steffen Koenig.

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Koenig, S., Zhu, B. From triangulated categories to abelian categories: cluster tilting in a general framework. Math. Z. 258, 143–160 (2008). https://doi.org/10.1007/s00209-007-0165-9

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  • DOI: https://doi.org/10.1007/s00209-007-0165-9

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