Rigid potentials for cluster algebras from double Bruhat cells

Maitreyee C. Kulkarni

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Rigid potentials for cluster algebras from double Bruhat cells

Maitreyee C. Kulkarni

Representation Theory · Submitted 4 Nov 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, we extend this result to the Berenstein-Fomin-Zelevinsky quivers corresponding to double Bruhat cells of symmetric Kac-Moody algebras.

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Buan, Iyama, Reiten and Smith proved that the superpotential of a quiver corresponding to an element of Coxeter group is rigid. In this paper, we extend this result to the Berenstein-Fomin-Zelevinsky quivers corresponding to double Bruhat cells of symmetric Kac-Moody algebras. We also realize these quivers as dimers models on cylinder over corresponding graphs.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Buan, Iyama, Reiten and Smith proved that the superpotential of a quiver corresponding to an element of Coxeter group is rigid.	background 1.00	0.02	0.04	asserted 1.00
s1	In this paper, we extend this result to the Berenstein-Fomin-Zelevinsky quivers corresponding to double Bruhat cells of symmetric Kac-Moody algebras.	contribution 0.87	0.92	0.79	asserted 1.00
s2	We also realize these quivers as dimers models on cylinder over corresponding graphs.	contribution 0.72	0.93	0.08	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

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Original abstract

Buan, Iyama, Reiten and Smith proved that the superpotential of a quiver corresponding to an element of Coxeter group is rigid. In this paper, we extend this result to the Berenstein-Fomin-Zelevinsky quivers corresponding to double Bruhat cells of symmetric Kac-Moody algebras. We also realize these quivers as dimers models on cylinder over corresponding graphs.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Using this structure on the quivers and the results from [ref] , we prove that BFZ quivers with their superpotentials are rigid QPs.

Dimer models on cylinders over Dynkin diagrams and cluster algebras · Introduction · 0.81

Cites as background 1 paper

These were defined by Postnikov [ref] and they encode information about seeds of the cluster algebra and its clusters.

Total positivity, Grassmannians, and networks · Introduction · 0.93

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