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
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朱林
ZHU Lin
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A是A2的路代数时给出其Auslander-Reiten箭图。
中图分类号:
[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. |
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