Non-kissing complexes for gentle algebras

Yann Palu; Vincent Pilaud; Pierre Guy Plamondon

Non-kissing complexes for gentle algebras

Yann Palu
, Vincent Pilaud
, Pierre Guy Plamondon

Université de Picardie Jules Verne
Laboratoire de Mathématiques d'Orsay

Research output: Contribution to conference › Paper › peer-review

Abstract

We introduce the non-kissing complex of any gentle bound quiver. This complex provides a powerful combinatorial model for support t-tilting theory over gentle algebras, and it generalizes and unifies the previously considered situations of quivers defined from subsets of the grid or from dissections of a polygon (both generalizing the classical associahedron). In this extended abstract, we report on lattice theoretic and geometric properties of finite non-kissing complexes: we show that their flip graphs are Hasse diagrams of congruence-uniform lattices, and that they can be realized by convex polytopes.

Original language	English
Publication status	Published - 1 Jan 2018
Event	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States Duration: 16 Jul 2018 → 20 Jul 2018

Conference

Conference	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018
Country/Territory	United States
City	Hanover
Period	16/07/18 → 20/07/18

Cite this

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title = "Non-kissing complexes for gentle algebras",

abstract = "We introduce the non-kissing complex of any gentle bound quiver. This complex provides a powerful combinatorial model for support t-tilting theory over gentle algebras, and it generalizes and unifies the previously considered situations of quivers defined from subsets of the grid or from dissections of a polygon (both generalizing the classical associahedron). In this extended abstract, we report on lattice theoretic and geometric properties of finite non-kissing complexes: we show that their flip graphs are Hasse diagrams of congruence-uniform lattices, and that they can be realized by convex polytopes.",

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AU - Pilaud, Vincent

AU - Plamondon, Pierre Guy

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N2 - We introduce the non-kissing complex of any gentle bound quiver. This complex provides a powerful combinatorial model for support t-tilting theory over gentle algebras, and it generalizes and unifies the previously considered situations of quivers defined from subsets of the grid or from dissections of a polygon (both generalizing the classical associahedron). In this extended abstract, we report on lattice theoretic and geometric properties of finite non-kissing complexes: we show that their flip graphs are Hasse diagrams of congruence-uniform lattices, and that they can be realized by convex polytopes.

AB - We introduce the non-kissing complex of any gentle bound quiver. This complex provides a powerful combinatorial model for support t-tilting theory over gentle algebras, and it generalizes and unifies the previously considered situations of quivers defined from subsets of the grid or from dissections of a polygon (both generalizing the classical associahedron). In this extended abstract, we report on lattice theoretic and geometric properties of finite non-kissing complexes: we show that their flip graphs are Hasse diagrams of congruence-uniform lattices, and that they can be realized by convex polytopes.

M3 - Paper

AN - SCOPUS:85089349644

T2 - 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018

Y2 - 16 July 2018 through 20 July 2018

ER -

Non-kissing complexes for gentle algebras

Abstract

Conference

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