English

Hereditary triangulated categories

Rings and Algebras 2019-02-19 v1 Representation Theory

Abstract

We call a triangulated category \emph{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.

Keywords

Cite

@article{arxiv.1606.08279,
  title  = {Hereditary triangulated categories},
  author = {Xiao-Wu Chen and Claus Michael Ringel},
  journal= {arXiv preprint arXiv:1606.08279},
  year   = {2019}
}
R2 v1 2026-06-22T14:35:11.368Z