Cluster scattering diagrams and theta basis for reciprocal generalized cluster algebras

Man Wai Cheung; Elizabeth Kelley; Gregg Musiker

Cluster scattering diagrams and theta basis for reciprocal generalized cluster algebras

Man Wai Cheung, Elizabeth Kelley, Gregg Musiker

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

Abstract

We give a construction of generalized cluster scattering diagrams, generalized cluster varieties, and theta bases for reciprocal generalized cluster algebras, the latter of which were defined by Chekhov and Shapiro. These constructions are analogous to the structures given for ordinary cluster algebras in the work of Gross, Hacking, Keel, and Kontsevich.

Original language	English (US)
Article number	#86
Journal	Seminaire Lotharingien de Combinatoire
Issue number	85
State	Published - 2021
Externally published	Yes

Bibliographical note

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© 2021, Seminaire Lotharingien de Combinatoire.All Rights Reserved.

Keywords

cluster algebra
generalized cluster algebra
scattering diagram
theta function

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title = "Cluster scattering diagrams and theta basis for reciprocal generalized cluster algebras",

abstract = "We give a construction of generalized cluster scattering diagrams, generalized cluster varieties, and theta bases for reciprocal generalized cluster algebras, the latter of which were defined by Chekhov and Shapiro. These constructions are analogous to the structures given for ordinary cluster algebras in the work of Gross, Hacking, Keel, and Kontsevich.",

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author = "Cheung, {Man Wai} and Elizabeth Kelley and Gregg Musiker",

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language = "English (US)",

journal = "Seminaire Lotharingien de Combinatoire",

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T1 - Cluster scattering diagrams and theta basis for reciprocal generalized cluster algebras

AU - Cheung, Man Wai

AU - Kelley, Elizabeth

AU - Musiker, Gregg

PY - 2021

Y1 - 2021

N2 - We give a construction of generalized cluster scattering diagrams, generalized cluster varieties, and theta bases for reciprocal generalized cluster algebras, the latter of which were defined by Chekhov and Shapiro. These constructions are analogous to the structures given for ordinary cluster algebras in the work of Gross, Hacking, Keel, and Kontsevich.

AB - We give a construction of generalized cluster scattering diagrams, generalized cluster varieties, and theta bases for reciprocal generalized cluster algebras, the latter of which were defined by Chekhov and Shapiro. These constructions are analogous to the structures given for ordinary cluster algebras in the work of Gross, Hacking, Keel, and Kontsevich.

KW - cluster algebra

KW - generalized cluster algebra

KW - scattering diagram

KW - theta function

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M3 - Article

AN - SCOPUS:85128071934

SN - 1286-4889

JO - Seminaire Lotharingien de Combinatoire

JF - Seminaire Lotharingien de Combinatoire

IS - 85

M1 - #86

ER -

Cluster scattering diagrams and theta basis for reciprocal generalized cluster algebras

Abstract

Bibliographical note

Keywords

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