A relation between tilting graphs and cluster-tilting graphs of hereditary algebras

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• 作者：Fang Li (1)
  Yichao Yang (1) (2)
  
  1. Department of Mathematics ; Zhejiang University (Yuquan Campus) ; Hangzhou ; 310027 ; China
  2. Department of Mathematics ; University of Sherbrooke ; Sherbrooke ; J1K 2R1 ; Canada
  
• 关键词：Tilting graph ; cluster ; tilting graph ; cluster category ; Stasheff polytope ; linear quiver ; 16G20 ; 16G70 ; 16D80
• 刊名：Frontiers of Mathematics in China
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：10
• 期：2
• 页码：275-291
• 全文大小：304 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576

文摘

We give the condition of isomorphisms between tilting graphs and cluster-tilting graphs of hereditary algebras. As a conclusion, it is proved that a graph is a skeleton graph of Stasheff polytope if and only if it is both the tilting graph of a hereditary algebra and also the cluster-tilting graph of another hereditary algebra. At last, when comparing such uniformity, the geometric realizations of simplicial complexes associated with tilting modules and cluster-tilting objects are discussed respectively.