Frontiers of Mathematics in China >

2015 , Vol. 10 >Issue 2: 275 - 291

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

RESEARCH ARTICLE

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

  • Fang LI 1 ,
  • Yichao YANG , 1,2
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  • 1. Department of Mathematics, Zhejiang University (Yuquan Campus), Hangzhou 310027, China
  • 2. Department of Mathematics, University of Sherbrooke, Sherbrooke J1K 2R1, Canada

Received date: 24 Jul 2013

Accepted date: 27 Aug 2014

Published date: 12 Feb 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Tilting graph; cluster-tilting graph; cluster category; Stasheff polytope; linear quiver

Cite this article

Fang LI , Yichao YANG . A relation between tilting graphs and cluster-tilting graphs of hereditary algebras[J]. Frontiers of Mathematics in China, 2015 , 10(2) : 275 -291 . DOI: 10.1007/s11464-015-0426-6

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