Ext-quivers of hearts of A-type and the orientations of associahedrons

JOURNAL OF ALGEBRA

卷:393

Article

Qiu, Yu

关键词: t-Structure;    Ext-quiver;    Binary tree;    Torsion pair;    Cluster theory;   

DOI  :  10.1016/j.jalgebra.2013.06.024

来源: Elsevier

【 摘 要 】

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 Gamma(N)A(n). This provides the classification for Buan-Thomas' colored quivers for higher clusters of A-type. We also give an explicit combinatorial constructions from a binary tree with n + 2 leaves to a torsion pair in mod k (A(n)) over right arrow; and a cluster tilting set in the corresponding cluster category, for the straight oriented A-type quiver (A(n)) over right arrow. As an application, we show that the orientation of the n-dimensional associahedron induced by poset structure of binary trees coincides with the orientation induced by poset structure of torsion pairs in mod k (A(n)) over right arrow (under the correspondence above). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free