Torsion Pairs and Quasi-abelian Categories

被引：0
作者：
Aran Tattar
机构：
[1] University of Leicester,School of Mathematics
来源：
Algebras and Representation Theory | 2021年 / 24卷
关键词：
Quasi-abelian category; Torsion class; Torsion pair; Harder-Narasimhan filtration; 18E05; 18E10; 19E40;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We define torsion pairs for quasi-abelian categories and give several characterisations. We show that many of the torsion theoretic concepts translate from abelian categories to quasi-abelian categories. As an application, we generalise the recently defined algebraic Harder-Narasimhan filtrations to quasi-abelian categories.
引用
收藏
页码：1557 / 1581
页数：24
相关论文
共 35 条
[1]  
Adachi T(2014)τ-tilting theory Compos. Math. 150 415-452
[2]  
Iyama O(1982)Faisceaux Pervers Soc. Math. France, Paris 100 5-171
[3]  
Reiten I(2006)Torsion theories in homological categories Journal of Algebra 305 18-47
[4]  
Beilinson A(2014)Affine Mirković-Vilonen polytopes Publications Mathématiques de l’IHÉS 120 113-205
[5]  
Bernstein J(2010)Exact categories Expo. Math. 28 1-69
[6]  
Deligne P(2003)Generators and representability of functors in commutative and noncommutative geometry Moscow Mathematical Journal 3 1-36
[7]  
Bourn D(1966)A torsion theory for abelian categories Trans. Am. Math. Soc. 121 223-235
[8]  
Gran M(1975)On the cohomology groups of moduli spaces of vector bundles on curves Math. Ann. 212 215-248
[9]  
Baumann P(2013)Stable categories of higher preprojective algebras Adv. Math. 244 23-68
[10]  
Kamnitzer J(2014)Reduction of τ-tilting modules and torsion pairs Int. Math. Res. Not. 2015 7190-7237
1234