《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (12): 69-75.doi: 10.6040/j.issn.1671-9352.0.2020.294
• • 上一篇
杨婷,谢云丽*
YANG Ting, XIE Yun-li*
摘要: 设D是三角范畴,A是D -容许的阿贝尔子范畴,证明了A的高维刚性子范畴在某些条件下诱导了D中的一个t-结构,并且该t-结构的心恰好就是A。
中图分类号:
[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. |
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