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

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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 cluster-tilting objects are discussed respectively.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University (Yuquan Campus), Hangzhou, 310027, China

    Fang Li & Yichao Yang

  2. Department of Mathematics, University of Sherbrooke, Sherbrooke, J1K 2R1, Canada

    Yichao Yang

Authors
  1. Fang Li
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  2. Yichao Yang
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Correspondence to Yichao Yang.

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Li, F., Yang, Y. A relation between tilting graphs and cluster-tilting graphs of hereditary algebras. Front. Math. China 10, 275–291 (2015). https://doi.org/10.1007/s11464-015-0426-6

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  • DOI: https://doi.org/10.1007/s11464-015-0426-6

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