Non-kissing complexes and tau-tilting for gentle algebras

IF 2 4区数学 Q1 MATHEMATICS

Memoirs of the American Mathematical Society Pub Date : 2017-07-24 DOI:10.1090/memo/1343

Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon

引用次数: 30

Abstract

We interpret the support τ \tau -tilting complex of any gentle bound quiver as the non-kissing complex of walks on its blossoming quiver. Particularly relevant examples were previously studied for quivers defined by a subset of the grid or by a dissection of a polygon. We then focus on the case when the non-kissing complex is finite. We show that the graph of increasing flips on its facets is the Hasse diagram of a congruence-uniform lattice. Finally, we study its g \mathbf {g} -vector fan and prove that it is the normal fan of a non-kissing associahedron.

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温柔代数的非接吻复形和tau倾斜

我们将任何温和束缚颤振的支持τ \tau倾斜复合物解释为在其开花颤振上行走的非亲吻复合物。特别相关的例子以前研究过由网格子集或多边形的解剖定义的颤振。然后我们关注非接吻复合体是有限的情况。我们证明了其面上增加翻转的图是同余一致格的哈塞图。最后，我们研究了它的g \mathbf {g}向量扇形，并证明了它是一个非接吻共轭面体的正规扇形。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Memoirs of the American Mathematical Society 数学-数学

CiteScore

3.50

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Memoirs of the American Mathematical Society is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS. To be accepted by the editorial board, manuscripts must be correct, new, and significant. Further, they must be well written and of interest to a substantial number of mathematicians.