Academic Report of School of Mathematical Sciences [2026] No. 075

(Series Report for High-Level University Construction No. 1334)

Title：Virasoro elements in conformal algebras

Speaker：Yucai Su, Professor (Jimei University and Tongji University)

Time：15:00-16:00, July 7, 2026

Location：Room 1425, Huiwen Building, Yuehai Campus, Shenzhen University

Abstract: It is well known that Virasoro elements play an extremely important role in the theory of vertex operator algebras, and likewise a very significant role in the field of conformal algebras. In this talk, we introduce the notion of a regular action in the category of conformal modules over Lie conformal algebras with Virasoro elements. We show that a finite conformal module over the general conformal algebra of rank 1 (resp., rank N with N>1) is semisimple if and only if there exists a pair of different Virasoro elements (resp., canonical Virasoro elements) with regular actions. Along the way to finding a semisimplicity criteria, we also discuss the classification of Virasoro elements of general conformal algebras, leading us to construct a huge number of new Virasoro conformal modules. This is a joint work with Chunguang Xia.

Speaker Profile：Yucai Su is a Distinguished Professor at Jimei University and Tongji University, a doctoral advisor, and a nationally recognized leading talent. In 2002, he was selected for the Ministry of Education’s “Talents Across the Centuries” Program; in 2005, he was selected for the Chinese Academy of Sciences’ “Hundred Talents Program”; and in 2012, he was named a Shanghai Outstanding Academic Leader. His research focuses primarily on Lie theory in algebra, conformal field theory in mathematical physics, and supersymmetry in theoretical physics. He has presided over numerous provincial and ministerial-level or higher research grants, including the National Natural Science Foundation of China’s Key Program, the General Program of the National Natural Science Foundation of China, and the Shanghai Outstanding Academic Leaders Program. He serves on the editorial boards of renowned domestic and international journals such as Algebra Colloquium, Journal of Mathematical Study, and the Acta Mathematica Sinica. He has published more than 100 papers in over 20 international journals, including J. Eur. Math. Soc., Adv. Math., Comm. Math. Phys., Proc. London Math. Soc., Math. Z., and Israel J. Math..

Faculty and students are welcome to attend!

Invited by: Jinkui Wan

School of Mathematical Sciences

July 2, 2026