您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

山东大学学报(理学版) ›› 2018, Vol. 53 ›› Issue (2): 1-8.doi: 10.6040/j.issn.1671-9352.0.2017.574

• •    下一篇

A4型箭图的可分单态射表示和RSS等价

朱林   

  1. 上海交通大学数学科学学院, 上海 200240
  • 收稿日期:2017-11-08 出版日期:2018-02-20 发布日期:2018-01-31
  • 作者简介:朱林(1990— ), 男, 博士研究生, 研究方向为代数表示论. E-mail:zhulin2323@163.com

Separated monic representations of quivers of type A4and RSS equivalences

ZHU Lin   

  1. School of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2017-11-08 Online:2018-02-20 Published:2018-01-31

摘要: 研究了A4型非线性定向箭图的可分单态射范畴与可分满态射范畴之间的RSS等价。利用组合和表示论的方法显式构造了RSS等价函子及其拟逆, 并在AA2的路代数时给出其Auslander-Reiten箭图。

关键词: 可分单态射表示, Ringel-Schmidmeier-Simson等价, Auslander-Reiten箭图

Abstract: Ringel-Schmidmeier-Simson equivalences between separated monomorphism categories and separated epimorphism categories when the quiver is the of type of A4 with nonlinear order is studied. Using combinatorial methods and representation tools, the equivalence and its quasi inverse are given explicitly, and also the Auslander-Reiten quiver when A is the path algebra of A2 is given.

Key words: Ringel-Schmidmeier-Simson equivalence, separated monic representations, Auslander-Reiten quiver

中图分类号: 

  • O153.3
[1] LUO Xiuhua, ZHANG Pu. Separated monic representation I: Gorenstein-projective modules[J]. J Algebra, 2017, 479:1-34.
[2] ASSEM I, SIMSON D, SKOWRONSKI A. Elements of the representation theory of associative algebras[M] // Techniques of representation theory, Lond Math Soc Students Texts 65. Cambridge: Cambridge University Press, 2006.
[3] AUSLANDER M, REITEN I, SMALØ S O. Representation theory of Artin algebras[M] // Cambridge Studies in Adv Math 36. Cambridge: Cambridge University Press, 1995.
[4] RINGEL C M. Tame algebras and integral quadratic forms[M] // Lecture Notes in Math:1099. New York: Springer-Verlag, 1984.
[5] KUSSIN D, LENZING H, MELTZER H. Nilpotent operators and weighted projective lines[J]. J Reine Angew Math, 2010, 685(6):33-71.
[6] KUSSIN D, LENZING H, MELTZER H, Triangle singularities, ADEchains, and weighted projective lines[J]. Adv Math, 2013, 237:194-251.
[7] RINGEL C M, SCHMIDMEIER M. Submodules categories of wild representation type[J]. J Pure Appl Algebra, 2006, 205(2):412-422.
[8] RINGEL C M, SCHMIDMEIER M. The Auslander-Reiten translation in submodule categories[J]. Trans Amer Math Soc, 2008, 360(2):691-716.
[9] RINGEL C M, SCHMIDMEIER M. Invariant subspaces of nilpotent operators I[J]. J Rein Angew Math, 2008, 614:1-52.
[10] SIMSON D. Linear representations of partially ordered sets and vector space categories[M]. [S.l] : Gordon and Breach Science Publishers, 1992.
[11] SIMSON D. Representation types of the category of subprojective representations of a finite poset over K[t] /(tm) and a solution of a Birkhoff type problem[J]. J Algebra, 2007, 311:1-30.
[12] SIMSON D. Tame-wild dichotomy of Birkhoff type problems for nilpotent linear operators[J]. J Algebra, 2015, 424:254-293.
[13] XIONG Baolin, ZHANG Pu, ZHANG Yuehui. Auslander-Reiten translations in monomorphism categories[J]. Forum Math, 2014, 26(3):863-912.
[14] XIONG Baolin, ZHANG Pu, ZHANG Yuehui. Bimodule monomorphism categories and RSS equivalences via cotilting modules[J]. arXiv: 1710.00314v1 [math.RT].
[15] BIRKHOFF G. Subgroups of abelian groups[J]. Proc Lond Math Soc II, 1934, 38:385-401.
[16] EIRIKSSON Ö. From submodule categories to the stable Auslander algebra[J]. J Algebra, 2017, 486:98-118.
[17] ZHANG Pu, XIONG Baolin. Separated monic representation II: frobenius subcategories and RSS equivalences[J]. arXiv:1707.04866v1 [math.RT].
[18] LESZCZYNSKI Z. On the representation type of tensor product algebras[J]. Fundamenta Math, 1994, 144:143-161.
[1] 吴小英,王芳贵. 分次版本的Enochs定理[J]. 山东大学学报(理学版), 2018, 53(10): 22-26.
[2] 程诚, 邹世佳. 一类Hopf代数的不可约可裂迹模[J]. 山东大学学报(理学版), 2018, 53(4): 11-15.
[3] 郭双建,李怡铮. 拟Hopf代数上BHQ何时是预辫子monoidal范畴[J]. 山东大学学报(理学版), 2017, 52(12): 10-15.
[4] 鹿道伟,王珍. 双代数胚上的L-R smash积[J]. 山东大学学报(理学版), 2017, 52(12): 32-35.
[5] 李金兰,梁春丽. 强Gorenstein C-平坦模[J]. 山东大学学报(理学版), 2017, 52(12): 25-31.
[6] 汪慧星,崔建,陈怡宁. 诣零*-clean环[J]. 山东大学学报(理学版), 2017, 52(12): 16-24.
[7] 孙彦中,杨晓燕. 相对于半对偶模的Gorenstein AC-投射模[J]. 山东大学学报(理学版), 2017, 52(10): 31-35.
[8] 马鑫,赵有益,牛雪娜. 复形的同伦分解的存在性及其同调维数[J]. 山东大学学报(理学版), 2017, 52(10): 18-23.
[9] 热比古丽·吐尼亚孜, 阿布都卡的·吾甫. 量子包络代数Uq(An)的Gelfand-Kirillov维数[J]. 山东大学学报(理学版), 2017, 52(10): 12-17.
[10] 陈秀丽,陈建龙. C-投射(内射,平坦)模与优越扩张[J]. 山东大学学报(理学版), 2017, 52(8): 85-89.
[11] 陈华喜, 许庆兵. Yetter-Drinfeld模范畴上 AMHH的弱基本定理[J]. 山东大学学报(理学版), 2017, 52(8): 107-110.
[12] 鲁琦,鲍宏伟. ZWGP-内射性与环的非奇异性[J]. 山东大学学报(理学版), 2017, 52(2): 19-23.
[13] 高汉鹏,殷晓斌. g(x)-J-Clean环[J]. 山东大学学报(理学版), 2017, 52(2): 24-29.
[14] 王尧,周云,任艳丽. 强2-好环[J]. 山东大学学报(理学版), 2017, 52(2): 14-18.
[15] 张子珩,储茂权,殷晓斌. GWCN环的若干性质[J]. 山东大学学报(理学版), 2016, 51(12): 10-16.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!