Cluster structures in 2-Calabi-Yau triangulated categories of Dynkin type with maximal rigid objects

doi:10.1007/s10114-017-6504-9

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	Cluster structures in 2-Calabi-Yau triangulated categories of Dynkin type with maximal rigid objects
	Chang, Hui Min 1,2
	2017-12-01
发表期刊	ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN	1439-8516
卷号	33 期号:12 页码:1693-1704
摘要	In this paper, we consider two kinds of 2-Calabi-Yau triangulated categories with finitely many indecomposable objects up to isomorphisms, called A (n,t) = D (b) (KA ((2t+1)(n+1)-3))/tau (t(n+1)-1)[1], where n, t 1, and D (n,t) = D (b) (KD (2t(n+1)))/tau ((n+1)) phi (n) , where n, t 1, and phi is induced by an automorphism of D (2t(n+1)) of order 2. Except the categories A (n,1), they all contain non-zero maximal rigid objects which are not cluster tilting. A (n,1) contain cluster tilting objects. We define the cluster complex of A (n,t) (resp. D (n,t) ) by using the geometric description of cluster categories of type A (resp. type D). We show that there is an isomorphism from the cluster complex of A (n,t) (resp. D (n,t) ) to the cluster complex of root system of type B (n) . In particular, the maximal rigid objects are isomorphic to clusters. This yields a result proved recently by Buan-Palu-Reiten: Let , resp. , be the full subcategory of A (n,t) , resp. D (n,t) , generated by the rigid objects. Then and as additive categories, for all t >= 1.
关键词	2-Calabi-Yau triangulated category cluster structure cluster complex
DOI	10.1007/s10114-017-6504-9
收录类别	SCIE
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000415354700010
出版者	SPRINGER HEIDELBERG
原始文献类型	Article
EISSN	1439-7617
引用统计	被引频次[WOS]：0 [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.library.ouchn.edu.cn/handle/39V7QQFX/25023
专题	国家开放大学
通讯作者	Chang, Hui Min
作者单位	1.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China; 2.Open Univ China, Sch Educ, Dept Appl Math, Beijing 100039, Peoples R China
推荐引用方式 GB/T 7714	Chang, Hui Min. Cluster structures in 2-Calabi-Yau triangulated categories of Dynkin type with maximal rigid objects[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2017,33(12):1693-1704.
APA	Chang, Hui Min.(2017).Cluster structures in 2-Calabi-Yau triangulated categories of Dynkin type with maximal rigid objects.ACTA MATHEMATICA SINICA-ENGLISH SERIES,33(12),1693-1704.
MLA	Chang, Hui Min."Cluster structures in 2-Calabi-Yau triangulated categories of Dynkin type with maximal rigid objects".ACTA MATHEMATICA SINICA-ENGLISH SERIES 33.12(2017):1693-1704.