Fundamental relations in quantum cluster algebras

报告人：陈学庆（美国威斯康星大学白水分校）

时  间：2026年7月22日10:00

地  点：海韵园实验楼S105

内容摘要:

Ringel discovered a remarkable way to construct the positive part of quantum group using the Hall algebra. Shortly thereafter, Lusztig observed that the Hall algebra can be understood in terms of functions on certain representation spaces. Via the sheaf-function correspondence, Lusztig obtained the canonical basis of the positive part of quantum group.

Cluster algebra was invented by Fomin and Zelevinsky in their purpose to study the total positivity and Lusztig’s dual canonical basis in coordinate ring and its q-deformation. Ringel proved that the Hall algebra satisfied so-called fundamental relations, which are similar to the quantum Serre relations. In this talk we will address the fundamental relations in an arbitrary quantum cluster algebra with principal coefficients, immediately and directly, we obtain an algebra homomorphism from the corresponding (untwisted) quantum group to this quantum cluster algebra.

This talk is based on the joint work with J. Huang, M. Ding and F. Xu.

个人简介：

陈学庆，美国威斯康星大学白水分校教授。研究领域为有限维代数（箭图）的表示、Hall代数与量子群、Cluster代数与量子Cluster代数。2002年博士毕业于加拿大卡尔顿大学，先后在加拿大渥太华大学及加拿大温莎大学从事科研工作。在包括Compositio Math., I.M.R.N., J. Algebra等期刊上发表过高水平论文30余篇。

联系人：阮诗佺