From recollement of triangulated categories to recollement of abelian categories

被引:0
作者
YaNan Lin
MinXiong Wang
机构
[1] Xiamen University,School of Mathematical Sciences
[2] Huaqiao University,School of Mathematical Sciences
来源
Science China Mathematics | 2010年 / 53卷
关键词
triangulated category; abelian category; recollement; tilting subcategory; quotient category; 16G20; 16G70; 19S99; 17B20;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper, we prove that if a triangulated category \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{D} $$\end{document} admits a recollement relative to triangulated categories \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{D}' $$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{D}'' $$\end{document}, then the abelian category \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{D}/\mathcal{T} $$\end{document} admits a recollement relative to abelian categories \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{D}'/i*(\mathcal{T}) $$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{D}''/j*(\mathcal{T}) $$\end{document} where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{T} $$\end{document} is a cluster tilting subcategory of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{D} $$\end{document} and satisfies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ i_* i^* (\mathcal{T}) \subset \mathcal{T},j_* j^* (\mathcal{T}) \subset \mathcal{T} $$\end{document}.
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页码:1111 / 1116
页数:5
相关论文
共 19 条
  • [1] Chen Q. H.(2003)Recollements of extension algebras Sci China Ser A 46 530-537
  • [2] Lin Y. N.(2008)Recollements, idempotent completions and t-structures of triangulated categories J Algebra 319 3053-3061
  • [3] Chen Q.(1988)Algebraic stratification in representation in representation categories J Algebra 117 504-521
  • [4] Tang L.(1988)Finite dimensional algebras and highest weight categories J Reine Angew Math 391 85-99
  • [5] Cline E.(2004)Comparison of abelian categories recollement Doc Math 9 41-56
  • [6] Parshall B.(2007)Higher dimensional Auslander-Reiten theory on maximal orthogonal subcategories Adv Math 210 22-50
  • [7] Scott L.(2008)From triangulated categories to abelian categories: cluster tilting in a general framework Math Z 258 143-160
  • [8] Cline E.(2008)One-point extension and recollement Sci China Ser A 51 376-382
  • [9] Parshall B.(1986)Elementary construction of perverse sheaves Invent Math 84 403-436
  • [10] Scott L.(undefined)undefined undefined undefined undefined-undefined