[1]张阳,林增强.Serre商范畴的Auslander-Reiten序列[J].华侨大学学报(自然科学版),2013,34(3):356-360.[doi:10.11830/ISSN.1000-5013.2013.03.0356]
　ZHANG Yang,LIN Zeng-qiang.Auslander-Reiten Sequences of Serre Quotient Categories[J].Journal of Huaqiao University(Natural Science),2013,34(3):356-360.[doi:10.11830/ISSN.1000-5013.2013.03.0356]
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Serre商范畴的Auslander-Reiten序列()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第34卷
期数:
2013年第3期
页码:
356-360
栏目:
出版日期:
2013-05-20

文章信息/Info

Title:
Auslander-Reiten Sequences of Serre Quotient Categories
文章编号:
1000-5013(2013)03-0356-05
作者:
张阳;  林增强
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
ZHANG Yang;  LIN Zeng-qiang
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
商范畴;  Auslander-Reiten序列;  垂范畴;  有限维k-代数
Keywords:
quotient category;  Auslander-Reiten sequence;  perpendicular category;  finite dimensional k-algebra
分类号:
O153.3;O154.1
DOI:
10.11830/ISSN.1000-5013.2013.03.0356
文献标志码:
A
摘要:
设A是有限维k-代数,A=A-mod,B是A的有厚度子范畴,通过从A的Auslander-Reiten(AR)序列到导出范畴Db(A)的AR三角的转化,研究A的AR序列与Serre商范畴A/B的AR序列的关系.文中给出A的AR序列在商函子Q∶A→A/B下的像是A/B的AR序列的充要条件.
Abstract:
Let A be a finite dimensional k-algebra, A be the category of finitely generated A-modules and B be a thick subcategory of A. This paper mainly discusses the relationship between the Auslander-Reiten(AR)sequences of A and A/B by transforming the AR-sequences of A to the AR-triangles of the bounded derived category of A. We get some necessary and sufficient conditions that the AR-sequences of A/B are induced by the AR-sequences of A.

参考文献/References:

[1] AUSLANDER M,SMAL? S O.Almost split sequences in subcategories[J].J Algebras,1981,69(2):426-454.
[2] AUSLANDER M, REITEN I, SMAL? S O. Representation theory of Artin algebras[M].Cambridge:Cambridge University Press,1995:136-185.
[3] PUIMAN N.Existence of Auslander-Reiten sequences in subcategories[J].J Pure and Applied Algebra,2011,215(10):2378-2384.
[4] HAPPEL D.Triangulated categories in the representation theory of finite dimensional algebras[M].Cambridge:Cambridge University Press,1988:31-34.
[5] HAPPEL D.Auslander-Reiten triangles in derived categories of finite-dimensionalalgebras[J].Proc Amer Math Soc,1991(12):641-648.
[6] J?RGENSEN P.Auslander-Reiten triangles in subcategories[J].J K Theory,2009(3):583-601.
[7] LIU Shi-ping.Auslander-Reiten theory in a Krull-Schmidt category[J].The Sao Paulo Journal of Mathematical Sciences,2010,4(3):425-472.
[8] 林增强.商范畴与AR三角[J].数学物理学报,2012,32(4):654-660.
[9] GABRIEL P.Des catégories abéliennes[J].Bull S M F,1962,90:323-448.
[10] MIYACHI J.Localization of triangulated categories and derived categories[J].J Algebra,1991,141(2):463-483.
[11] BEILINSON A A,BERNSTEIN J,DELIGNE P.Faisceaux perverse[J].Astérisque,1982,100:5-171.

备注/Memo

备注/Memo:
收稿日期: 2012-05-12
通信作者: 林增强(1980-),男,副教授,主要从事代数表示论的研究.E-mail:lzq134@163.com.
基金项目: 国家自然科学基金资助项目(11126331); 福建省自然科学基金资助项目(2011J01004)
更新日期/Last Update: 2013-05-20