The Exchange Quiver of Cluster Algebras and the Exchange

 Quiver of Root Systems

报告专家:行田康晃(The University of Tokyo)



报告摘要In 2002, Fomin and Zelevinsky classified cluster algebras of finite type by using Dynkin root systems. In the proof of this classification, they established a bijection between cluster variables and almost positive roots, demonstrating that it induces a graph isomorphism between the exchange graph of clusters and that of c-clusters. This graph isomorphism now plays a crucial role in connecting cluster algebra theory with Lie theory.

    In recent times, the exchange graph of clusters (and c-clusters, respectively) has been given a "natural" orientation in cluster algebra theory (and Lie theory). In this presentation, I will demonstrate that these orientations are preserved by the graph isomorphism provided by Fomin and Zelevinsky.

专家简介行田康晃,东京大学数理科学研究院特別研究员PD,主要从事丛代数方面的研究,目前在 Annals of Combinatorics,  Annales de l’institut Fourier, IMRN, SIGMA等国际重要期刊上发表论文数篇。