Polytopal realizations of finite type g-vector fans

Christophe Hohlweg; Vincent Pilaud; Salvatore Stella

doi:10.1016/j.aim.2018.01.019

Polytopal realizations of finite type g-vector fans

Christophe Hohlweg
, Vincent Pilaud
, Salvatore Stella

Research output: Contribution to journal › Article › peer-review

Abstract

This paper shows the polytopality of any finite type g-vector fan, acyclic or not. In fact, for any finite Dynkin type Γ, we construct a universal associahedron Asso_un(Γ) with the property that any g-vector fan of type Γ is the normal fan of a suitable projection of Asso_un(Γ).

Original language	English
Pages (from-to)	713-749
Number of pages	37
Journal	Advances in Mathematics
Volume	328
DOIs	https://doi.org/10.1016/j.aim.2018.01.019
Publication status	Published - 13 Apr 2018

Keywords

Cluster algebras
Generalized associahedra

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10.1016/j.aim.2018.01.019

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title = "Polytopal realizations of finite type g-vector fans",

abstract = "This paper shows the polytopality of any finite type g-vector fan, acyclic or not. In fact, for any finite Dynkin type Γ, we construct a universal associahedron Assoun(Γ) with the property that any g-vector fan of type Γ is the normal fan of a suitable projection of Assoun(Γ).",

keywords = "Cluster algebras, Generalized associahedra",

author = "Christophe Hohlweg and Vincent Pilaud and Salvatore Stella",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

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AU - Hohlweg, Christophe

AU - Pilaud, Vincent

AU - Stella, Salvatore

PY - 2018/4/13

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N2 - This paper shows the polytopality of any finite type g-vector fan, acyclic or not. In fact, for any finite Dynkin type Γ, we construct a universal associahedron Assoun(Γ) with the property that any g-vector fan of type Γ is the normal fan of a suitable projection of Assoun(Γ).

AB - This paper shows the polytopality of any finite type g-vector fan, acyclic or not. In fact, for any finite Dynkin type Γ, we construct a universal associahedron Assoun(Γ) with the property that any g-vector fan of type Γ is the normal fan of a suitable projection of Assoun(Γ).

KW - Cluster algebras

KW - Generalized associahedra

U2 - 10.1016/j.aim.2018.01.019

DO - 10.1016/j.aim.2018.01.019

M3 - Article

AN - SCOPUS:85042744307

SN - 0001-8708

VL - 328

SP - 713

EP - 749

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Polytopal realizations of finite type g-vector fans

Abstract

Keywords

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