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arXiv · 1606.08279

Hereditary triangulated categories

Xiao-Wu Chen·Claus Michael Ringel
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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.

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Xiao-Wu Chen, Claus Michael Ringel. 2016-06-27. Hereditary triangulated categories. https://arxiv.org/abs/1606.08279

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