Non-kissing complexes and tau-tilting for gentle algebrasThanks: The three authors were partially supported by the French ANR grant SC3A (15 CE40 0004 01).
Yann Palu Yann PaluLAMFA, Université Picardie Jules Verne, Amiens Email address: URL: http://www.lamfa.u-picardie.fr/palu/ , Vincent Pilaud Vincent PilaudCNRS、LIX, École Polytechnique, Palaiseau Email address: URL: http://www.lix.polytechnique.fr/˜pilaud/ and Pierre-Guy Plamondon Pierre-Guy PlamondonUniversité Paris-Saclay, UVSQ, CNRS, Laboratoire de Mathématiques de Versailles Email address: URL: https://www.imo.universite-paris-saclay.fr/˜plamondon/
Abstract
We interpret the support $\tau$ -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 $\mathbf{g}$ -vector fan and prove that it is the normal fan of a non-kissing associahedron.
原文 arXiv:1707.07574;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1707.07574v4