JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (12): 69-75.doi: 10.6040/j.issn.1671-9352.0.2020.294

Previous Articles    

Higher rigid subcategories and t-structures

YANG Ting, XIE Yun-li*   

  1. School of Mathematics, Southwest Jiaotong University, Chengdu 611756, Sichuan, China
  • Published:2020-12-01

Abstract: Let D be a triangulated category and A a D -admissible abelian subcategory of D. This paper shows that under some conditions a higher rigid subcategory of A induces a t-structure on D whose heart is just A.

Key words: triangulated category, d-rigid subcategory, t-structure

CLC Number: 

  • O154.1
[1] HAPPEL D, REITEN I, SMALØ S O. Tilting in abelian categories and quasitilted algebras[J]. Memoirs of the American Mathematical Society, 1996, 120(575):1-88.
[2] HOSHINO M, KATO Y, MIYACHI J. On t-structures and torsion theories induced by compact objects[J]. Journal of Pure and Applied Algebra, 2002, 167(1):15-35.
[3] IYAMA O, YANG D. Silting reduction and Calabi-Yau reduction of triangulated categories[J]. Transactions of the American Mathematical Society, 2018, 370(11):7861-7898.
[4] BAZZONI S. The t-structure induced by an n-tilting module[J]. Transactions of the American Mathematical Society, 2019, 371(9):6309-6340.
[5] 谢云丽. 由生成子范畴导出的t-结构[J]. 四川大学学报(自然科学版),2008,45(5):1037-1042. XIE Yunli. t-Structure arising from a generating subcategory[J]. Journal of Sichuan University(Natural Science Edition), 2008, 45(5):1037-1042.
[6] AUSLANDER M, SMALØ S O. Almost split sequences in subcategories[J]. Journal of Algebra, 1981, 69(2):426-454.
[7] JASSO G, KÜLSHAMMER J, PSAROUDAKIS C, et al. Higher Nakayama algebras I: construction[J]. Advances in Mathematics, 2019, 351:1139-1200.
[8] IYAMA O. Auslander correspondence[J]. Advances in Mathematics, 2007, 210(1):51-82.
[9] IYAMA O. Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories[J]. Advances in Mathematics, 2007, 210(1):22-50.
[10] JØRGENSEN P. Torsion classes and t-structures in higher homological algebra[J]. International Mathematics Research Notices, 2016, 2016(13):3880-3905.
[11] NEEMAN A. Triangulated categories[M]. Princeton: Princeton University Press, 2001.
[12] KELLER B, VOSSIECK D. Aisles in derived categories[J]. Bull Soc Math Belg Sér A, 1988, 40(2):239-253.
[1] ZHENG Min, CHEN Qing-hua. Ki-group of t-structure of triangulated category [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(8): 48-53.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!