On the properties of the exchange graph of a cluster algebra

• Autores: Michael Gekhtman, Michael Shapiro, Alek Vainshtein
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 2-3, 2008, págs. 321-330
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n2.a10
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• Resumen

  • We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra $\A$ in two cases: when $\A$ is of geometric type and when $\A$ 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 $\A$. Both conjectures were formulated recently by Fomin and Zelevinsky.