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A relation between tilting graphs and cluster-tilting graphs of hereditary algebras |
Fang LI1,Yichao YANG1,2,*( ) |
1. Department of Mathematics, Zhejiang University (Yuquan Campus), Hangzhou 310027, China
2. Department of Mathematics, University of Sherbrooke, Sherbrooke J1K 2R1, Canada |
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Abstract 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 clustertilting objects are discussed respectively.
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Tilting graph
cluster-tilting graph
cluster category
Stasheff polytope
linear quiver
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Corresponding Author(s):
Yichao YANG
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Issue Date: 12 February 2015
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