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Mathematische Zeitschrift

, Volume 258, Issue 1, pp 143–160 | Cite as

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

  • Steffen KoenigEmail author
  • Bin Zhu
Article

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.

Keywords

Triangulated categories Abelian categories 1-Orthogonal categories Tilting Cluster categories Gorenstein algebras 

Mathematics Subject Classification (2000)

16G20 16G70 19S99 17B20 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität zu KölnKölnGermany
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingPeople’s Republic of China

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