Speaker: Professor Hui Changchang
Topic: On Tachikawa’s second conjecture
Date: March 8th, 2024 (Friday)
Time: 2.00-3.00 p.m.
Venue: Academic Lecture Hall 1508, Jingyuan Building
Sponsors: School of Mathematics and Statistics, Institute of Mathematics, Institute of Science and Technology
Biography:
Hui Changchang is a distinguished professor at the School of Mathematical Sciences at Capital Normal University, a doctoral advisor, and a national high-level talent. He mainly engaged in research on algebraic representation theory, and has published more than 90 papers in internationally renowned journals such as J.Rein Ang.Math., Adv.Math., Proc.London Math. Soc., Trans Amer Math. Soc., J.Algebra, J.Pure Appl.Algebra, etc. Now, he is the editorial board member of J.Algebra and Archiv der Mathematik. He has won the Second Prize of the Ministry of Education Science and Technology Progress and the Friedrich Wilhelm Bessel Research Award.
Abstract:
In the representation theory and homological algebra of finite-dimensional algebras, one of the most prominent conjectures is the long-standing and not yet solved Nakayama conjecture, saying that a finite-dimensional algebra over a field with infinite dominant dimension should be selfinjective. This conjecture is equivalent to the combination of two conjectures by Tachikawa, where the second conjecture states that an orthogonal module over a self-injective algebra should be projective. In this talk we consider Tachikawa’s second conjecture for symmetric algebras. We give a new formulation of this conjecture for symmetric algebras in terms of derived recollements of algebras. The talk presents parts of a joint work with H. X. Chen and M. Fang.