School of Mathematical Sciences Academic Report [2025] No. 018

(High-Level University Construction Series Report No. 1041)

Lecture Title: Cohomology Theory of Difference Lie Groups

Speaker: Assoc. Prof. Li Yunnan (Guangzhou University)

Date & Time: 3:00–4:00 PM, March 27, 2025

Venue: Huixing Building Room 514, Shenzhen University

Abstract: A difference Lie group is a Lie group equipped with a difference operator, equivalently a crossed homomorphism with respect to the adjoint action. In this talk, we first introduce the concept of representations of difference Lie groups and establish the relationship between their representations and those of difference Lie algebras through differentiation and integration. We then develop a cohomology theory for difference Lie groups, justified by the van Est theorem. As applications, all abelian extensions of difference Lie groups are classified using the second cohomology group. This is joint work with Jun Jiang and Yunhe Sheng.

Biography: Assoc. Prof. Li Yunnan is a master’s supervisor in the School of Mathematics and Information Science at Guangzhou University. His research focuses on Lie algebras, quantum groups, and algebraic combinatorics. He has published more than ten academic papers in internationally renowned mathematical journals such as Mathematische Zeitschrift, Pacific Journal of Mathematics, Journal of Combinatorial Theory, Series A., Journal of Algebra, Journal of Algebraic Combinatorics.

All faculty and students are welcome to attend!

Invited by: Xiao Wei

School of Mathematical Sciences

March 25, 2025