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。