On the properties of the exchange graph of a cluster algebra

Michael Gekhtman; Michael Shapiro; Alek Vainshtein

doi:10.4310/MRL.2008.v15.n2.a10

On the properties of the exchange graph of a cluster algebra

Michael Gekhtman, Michael Shapiro, Alek Vainshtein

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

Abstract

We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra script A in two cases: when script A is of geometric type and when script A is arbitrary and its exchange matrix is nondegenerate. In the second case we also prove that the exchange graph does not depend on the coefficients of script A. Both conjectures were formulated recently by Fomin and Zelevinsky.

Original language	English
Pages (from-to)	321-330
Number of pages	10
Journal	Mathematical Research Letters
Volume	15
Issue number	2-3
DOIs	https://doi.org/10.4310/MRL.2008.v15.n2.a10
State	Published - 2008

Keywords

Cluster algebra
Compatible 2-form
Exchange graph

ASJC Scopus subject areas

General Mathematics

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10.4310/MRL.2008.v15.n2.a10

Cite this

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abstract = "We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra script A in two cases: when script A is of geometric type and when script A is arbitrary and its exchange matrix is nondegenerate. In the second case we also prove that the exchange graph does not depend on the coefficients of script A. Both conjectures were formulated recently by Fomin and Zelevinsky.",

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AB - We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra script A in two cases: when script A is of geometric type and when script A is arbitrary and its exchange matrix is nondegenerate. In the second case we also prove that the exchange graph does not depend on the coefficients of script A. Both conjectures were formulated recently by Fomin and Zelevinsky.

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KW - Compatible 2-form

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DO - 10.4310/MRL.2008.v15.n2.a10

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On the properties of the exchange graph of a cluster algebra

Abstract

Keywords

ASJC Scopus subject areas

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