On the uniqueness of stratifications of derived module categories
Representation Theory
2012-02-10 v4 Rings and Algebras
Abstract
Recollements of triangulated categories may be seen as exact sequences of such categories. Iterated recollements of triangulated categories are analogues of geometric or topological stratifications and of composition series of algebraic objects. We discuss the question of uniqueness of such a stratification, up to ordering and derived equivalence, for derived module categories. The main result is a positive answer in the form of a Jordan H\"older theorem for derived module categories of hereditary artin algebras. We also provide examples of derived simple rings.
Keywords
Cite
@article{arxiv.1006.5301,
title = {On the uniqueness of stratifications of derived module categories},
author = {Lidia Angeleri Hügel and Steffen Koenig and Qunhua Liu},
journal= {arXiv preprint arXiv:1006.5301},
year = {2012}
}