Hereditary triangulated categories

  • Xiao-Wu Chen

    University of Science and Technology of China, Hefei, China
  • Claus Michael Ringel

    Universität Bielefeld, Germany, and Jiao Tong University, Shanghai, China


We call a triangulated category hereditary provided that it is equivalent to the bounded derived category of a hereditary abelian category, where the equivalence is required to commute with the translation functors. If the triangulated category is algebraical, we may replace the equivalence by a triangle equivalence. We give two intrinsic characterizations of hereditary triangulated categories using a certain full subcategory and the non-existence of certain paths. We apply them to piecewise hereditary algebras.

Cite this article

Xiao-Wu Chen, Claus Michael Ringel, Hereditary triangulated categories. J. Noncommut. Geom. 12 (2018), no. 4, pp. 1425–1444

DOI 10.4171/JNCG/311