Decomposition of torsion pairs on module categories

2012/05/07 by Fan Kong, Kong, Fan, Keyan Song +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras #math.RT

paper · pdf · doi:10.48550/arxiv.1205.1324

arxiv created 2012/05/07 · openalex publication_date 2012/05/07 · arxiv updated 2012/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we generalize the concept of torsion pairs and study its structure. As a trial of obtaining all torsion pairs, we decompose torsion pairs by projective modules and injective modules. Then we calculate torsion pairs on the algebra KAn and tub categories. At last we try to find all torsion pairs on the module categories of finite dimensional hereditary algebras.

Citations

• On a triangulated category which behaves like a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon

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