Stratifications of algebras with two simple modules

2013/10/13 by Qunhua Liu, Dong Yang, Liu, Qunhua +1 · 2 citations
Mathematics · Physics and Astronomy · #16E35 #16E40 #16E45 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1310.3480

openalex publication_date 2013/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a finite-dimensional algebra with two simple modules. It is shown that if the derived category of A admits a stratification with simple factors being the base field k, then A is derived equivalent to a quasi-hereditary algebra. As a consequence, if further k is algebraically closed and A has finite global dimension, then A is either derived simple or derived equivalent to a quasi-hereditary algebra

Cited by

• Examples of tilting-discrete symmetric algebras
• On compact exceptional objects in derived module categories

Related

• On the derived category of quasi-hereditary algebras with two simple modules
• A generalization of the theory of standardly stratified algebras I: Standardly stratified ringoids
• Stratifying systems over hereditary algebras
• Stratifications of derived categories from tilting modules over tame hereditary algebras
• On good filtration dimensions for standardly stratified algebras