Non-kissing complexes and tau-tilting for gentle algebras - Université de Versailles Saint-Quentin-en-Yvelines Access content directly
Journal Articles Memoirs of the American Mathematical Society Year : 2021

Non-kissing complexes and tau-tilting for gentle algebras

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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Dates and versions

hal-04446762 , version 1 (08-02-2024)

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Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon. Non-kissing complexes and tau-tilting for gentle algebras. Memoirs of the American Mathematical Society, 2021, 274 (1343), ⟨10.1090/memo/1343⟩. ⟨hal-04446762⟩
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