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	Cluster combinatorics of d-cluster categories
	Zhou, Yu ; Zhu, Bin
	2010-10-12 ; 2010-10-12
关键词	d-Cluster tilting objects d-Cluster categories Complements Generalized cluster complexes CALABI-YAU CATEGORIES TRIANGULATED CATEGORIES TILTED ALGEBRAS TILTING THEORY MUTATION MODULES Mathematics
中文摘要	We study the cluster combinatorics of d-cluster tilting objects in d-cluster categories. Using mutations of maximal rigid objects in d-cluster categories, which are defined in a similar way to mutations for d-cluster tilting objects, we prove the equivalences between d-cluster tilting objects, maximal rigid objects and complete rigid objects. Using the chain of d + 1 triangles of d-cluster tilting objects in 10. Iyama, Y. Yoshino, Mutations in triangulated categories and rigid Cohen-Macaulay modules, Invent. Math. 172 (1) (2008) 117-168], we prove that any almost complete d-cluster tilting object has exactly d + I complements, compute the extension groups between these complements, and study the middle terms of these d + 1 triangles. All results are the extensions of corresponding results on cluster tilting objects in cluster categories established for d-cluster categories in [A. Buan, R. Marsh, M. Reineke, I. Reiten, G. Todorov, Tilting theory and cluster combinatorics, Adv. Math. 204 (2006) 572-618]. They are applied to the Fomin-Reading generalized cluster complexes of finite root systems defined and studied in [S. Fomin, N. Reading, Generalized cluster complexes and Coxeter combinatorics, Int. Math. Res. Not. 44 (2005) 2709-2757; H. Thomas, Defining an m-cluster category, J. Algebra 318 (2007) 37-46; K. Baur, R. Marsh, A geometric description of m-cluster categories, Trans. Amer. Math. Soc. 360 (2008) 5789-5803; K. Baur, R. Marsh, A geometric description of the m-cluster categories of type D-n, preprint. arXiv:math.RT/0610512; see also Int. Math. Res. Not. 2007 (2007), doi:10.1093/imrn/rnm011], and to that of infinite root systems [B. Zhu, Generalized cluster complexes via quiver representations, J. Algebraic Combin. 27 (2008) 25-54]. (C) 2009 Elsevier Inc. All rights reserved.
语种	英语 ; 英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE ; SAN DIEGO ; 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/81324]
专题	清华大学
推荐引用方式 GB/T 7714	Zhou, Yu,Zhu, Bin. Cluster combinatorics of d-cluster categories[J],2010, 2010.
APA	Zhou, Yu,&Zhu, Bin.(2010).Cluster combinatorics of d-cluster categories..
MLA	Zhou, Yu,et al."Cluster combinatorics of d-cluster categories".(2010).

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