报告题目：Vertex algebras, Conformal Lie algebras, and cocommutative vertex bialgebras
时 间：2026年07月27日 (星期一) 10：00
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）
参加对象：感兴趣的老师和研究生
报告摘要：This talk is on the interactions among vertex algebras, vertex Lie algebras, and vertex bialgebras. From deffnition, every vertex algebra is naturally a conformal Lie algebra, namely a vertex Lie algebra. On the other hand, it is known that associated to every conformal Lie algebra C one has an authentic Lie algebra CLie, and furthermore has a canonical vertex algebra VC with U(CLie) as its underlying space. We show that VC is a connected cocommutative vertex bialgebra. On the other hand, for a general vertex bialgebra V , we show that the set P(V ) of primitive elements is a vertex Lie algebra. Furthermore, we show that if V is a connected cocommutative vertex bialgebra, then V is isomorphic to the vertex bialgebra VP(V ) associated to the vertex Lie algebra P(V ). In particular, this shows that every cocommutative connected vertex bialgebra V is isomorphic to VP(V ) and hence establishes the equivalence between the category of cocommutative connected vertex bialgebras and the category of vertex Lie algebras. This talk is partially based on a joint work with Jianzhi Han and Yukun Xiao.
报告人简介：李海生，美国罗格斯大学肯顿分校终身教授，著名华人数学家、顶点算子代数奠基人之一，多年来一直从事无穷维李代数、顶点代数、顶点算子代数的重要表示与结构理论的研究。在Duke Math. J.、Adv. Math.、Math. Ann.、Comm. Math. Phys.、Trans. Amer. Math. Soc.、Israel J. Math.、Math. Z.、Selecta Math. (N.S.)、J. Algebra、J. Pure Appl. Algebra等著名期刊发表高水平学术论文100余篇，被同行文章引用超3000篇次，并担任Electronic Research Archive杂志的编委。主持多项美国自然科学基金，一项中国自然科学基金（海外合作项目）。