Ext-quivers of hearts of A-type and the orientation of associahedron

Yu Qiu Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, United Kingdom

Representation Theory mathscidoc:2206.30006

Journal of Algebra, 393, (1), 60-70, 2013.11
We classify the Ext-quivers of hearts in the bounded derived category D(A_n) and the finite-dimensional derived category D(\Gamma_N A_n) of the Calabi-Yau-N Ginzburg algebra D(\Gamma_N A_n). This provides the classification for Buan-Thomas' colored quiver for higher clusters of A-type. We also give explicit combinatorial constructions from a binary tree with n+2 leaves to a torsion pair in mod k\overrightarrow{A_n} and a cluster tilting set in the corresponding cluster category, for the straight oriented A-type quiver \overrightarrow{A_n}. As an application, we show that the orientation of the n-dimensional ssociahedron induced by poset structure of binary trees coincides with the orientation induced by poset structure of torsion pairs in mod k\overrightarrow{A_n} (under the correspondence above).
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@inproceedings{yu2013ext-quivers,
  title={Ext-quivers of hearts of A-type and the orientation of associahedron},
  author={Yu Qiu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626163800107954461},
  booktitle={Journal of Algebra},
  volume={393},
  number={1},
  pages={60-70},
  year={2013},
}
Yu Qiu. Ext-quivers of hearts of A-type and the orientation of associahedron. 2013. Vol. 393. In Journal of Algebra. pp.60-70. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626163800107954461.
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