Jordan Hölder theorems for derived module categories of piecewise hereditary algebras

2011/04/18 by Lidia Angeleri Hügel, Hügel, Lidia Angeleri, Steffen Koenig +3
Mathematics · #16E30 #16G30 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #math.RT #msc:16E30 #msc:16G30 #msc:18E30

paper · pdf · doi:10.48550/arxiv.1104.3418

21 pages

arxiv created 2011/04/18 · openalex publication_date 2011/04/18 · arxiv updated 2011/04/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A Jordan Hölder theorem is established for derived module categories of piecewise hereditary algebras. The resulting composition series of derived categories are shown to be independent of the choice of bounded or unbounded derived module categories, and also of the choice of finitely generated or arbitrary modules.

Citations

• Recollements and tilting objects

Related

• Derived categories of quasi-hereditary algebras and their derived\n composition series
• Jordan-Hölder theorem for finite dimensional Hopf algebras
• A simple counterexample to the Jordan-Hölder property for derived categories
• On the uniqueness of stratifications of derived module categories
• Ladders and simplicity of derived module categories