Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists

Ishibashi, Tsukasa

doi:10.3842/sigma.2020.025

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2021

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Cited by 1 publication

(2 citation statements)

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“…For general quivers, this can be very difficult since the mutation class can be infinite. When the quiver in question has finitely many quivers in its mutation class, there is an algorithmic construction of the cluster modular group, see Ishibashi's paper [13]. We present a simplified version of the algorithm which only computes a generating set without computing all the relations.…”

Section: 2mentioning

confidence: 99%

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Cluster Modular Groups of Affine and Doubly Extended Cluster Algebras

Kaufman,

Greenberg

2021

Preprint

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We calculate the cluster modular groups of affine and doubly extended type cluster algebras in a uniform way by introducing a new family of quivers. We use this uniform description to construct a natural finite quotient of the cluster complex of each affine and doubly extended cluster algebra. Using this construction, we introduce the notion of affine and doubly extended generalized associahedra, and count their facets. Contents 1. Introduction 1 2. Preliminaries on Dynkin Diagrams, Quivers, and Mutations 3 3. The Cluster Modular Group 8 4. Type T n,w Cluster Algebras 11 5. Affine Cluster Algebras 15 6.

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Section: 2mentioning

confidence: 99%

“…Note, unlike the graph in [13], in our formulation the degree of each node is the rank of the cluster algebra.…”

Section: 2mentioning

confidence: 99%