Speaker: 肖杰教授，北京师范大学数学科学学院

Title: Root categories and Lie groups

Language: Chinese

Time & Venue: 2026.09.09 15:30-17:00 南楼N204 Zoom Meeting ID：898 1872 6621 密码：123456

Abstract: D. Happel introduced the root category as a two-periodic orbit triangulated category R of the derived category of Dynkin quiver. The Gabriel Theorem can be stated with the Auslander-Reiten quiver of R, not only for the positive roots Φ^+ but also the whole root system Φ. We introduce here a process to build up semi-simple Lie algebras and Chevalley groups via Hall algebra approach. The construction can be applied to a realization of compact real form and maximal compact subgroups from the root category R, and obtain the Peter-Weyl Theorem and the Plancherel Theorem for compact groups. This is a joint work with Buyan Li.