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

Y. Qiu

Research output: Contribution to journalArticle

Abstract

We classify the Ext-quivers of hearts in the bounded derived category D(An) and the finite-dimensional derived category D(NAn) of the Calabi-Yau-N Ginzburg algebra . 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 modkAn→ and a cluster tilting set in the corresponding cluster category, for the straight oriented A-type quiver An→. 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 modkAn→ (under the correspondence above).
Original languageEnglish
Pages (from-to)60-70
Number of pages11
JournalJournal of Algebra
Volume393
DOIs
Publication statusPublished - 1 Nov 2013

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