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Q-复形和三角范畴 被引量：3

Q-Complexes and triangulated categories
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摘要 作者定义了Q-复形范畴,它是两类重要的范畴的推广,一类是通常意义下的复形范畴,另一类是重复代数的模范畴;然后证明了在一定条件下Q-复形范畴是Frobenius范畴,从而其稳定范畴是三角范畴;最后刻画了重复代数的模范畴的稳定范畴里的一个满子范畴,并且证明了其上存在Auslander-Reiten三角. The category of Q-complexes are defined, which generalizes two kinds of important categories. One is the category of differential complexes or simply complexes as usual, the other is the category of modules of repetitive algebras. Then the relationship between the stable category of Q-complexes and a triangulated category is discussed. And based on this a full subcatgory of the category of modules of repetitive algebras is found out, some relationship with the derived category are obtained.
作者 刘品 谢云丽
机构地区 四川大学数学学院 西南交通大学数学系
出处 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2008年第4期709-714,共6页 Journal of Sichuan University(Natural Science Edition)
基金 国家自然科学基金"973"项目(0020105409002)
关键词 Q-复形 导出范畴 三角范畴 重复代数的模范畴 Q-complexes, derived categories, triangulated categories
分类号 O154.1 [理学—基础数学]
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参考文献7

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同被引文献27

  • 1Fomin S, Zelevinsky A. Cluster algebra I : Foundations [J]. J Amer Math Soe, 2002, 15,(2): 497.
  • 2Fomin S, Zelevinsky A. Cluster algebra Ⅱ : Finitetype classification [J]. Invent Math, 2003, 154: 63.
  • 3Buan A, Marsh R, Reineke M. Tilting theory and cluster combinatorics [J]. Adv Math, 2006, 204: 572.
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  • 7Keller B. Triangulated orbit categories [J]. Documenta Math, 2005, 10: 551.
  • 8Barot M, Kussin D, Lenzing H. The grothendieck group of a cluster category[J]. J Pure Applied Algebra, 2008, 212: 33.
  • 9Hanppel D. Triangulated categories in the representation theory of finite dimensional algebras IMP. Cambridge: Cambridge University Press, 1988.
  • 10Xiao J, Zhu B. Relations for the grothendieck groups of triangulated category [J]. J Algebra, 2002, 257: 37.

引证文献3

二级引证文献6

四川大学学报（自然科学版）
2008年 第4期

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