题目：dg Vertex Algebras over General Commutative Rings and Almost dg Poisson Algebras

报告人：林宗柱 教授（美国堪萨斯州立大学）

地点：致远楼108室

时间：2025年7月5日 16:00–17:00

Abstract: Vertex algebras are mathematical models for 2-dimensional conformal field theory. A vertex algebra gives a family of binary operations on a vertex space satisfying a set of complicated conditions. These operations are neither associative nor a Lie operation. Packing them together, one gets a field for each vector over a curve in the physical setting. These fields should be commutative if the points are distinct. Using this as motivation, we define a differential graded vertex algebra over an arbitrary commutative ring k by constructing a symmetric tensor category of differential complexes over the tensor category of D-modules over arbitrary commutative ring k. Instead of taking D as the universal enveloping algebra of the Lie algebra of the group R, we take the distribution algebra of the k-group scheme Ga. The algebra D has a divided power structure (pd-structure) which defines a linear topology. The category we consider should be the category of discrete D-modules with continuous morphisms. There are two special algebraic structures associated with a vertex algebra corresponding to the 0-mode (which gives an almost Lie algebra) and the (-1)-mode (which gives an almost associative algebra structure). These two algebraic structures give an almost Poisson structure. We will show that there is a left adjoint functor to the forgetful functor from the category of vertex algebras to the category of almost Poisson algebra. The category is closely related to the Chiral category constructed by Beilinson and Drinfeld.

报告人简介：林宗柱，美国堪萨斯州立大学（Kansas State University）终身教授，曾任美国科学基金会NSF项目主任和《中国科学：数学》编委。主要从事代数表示论等方面的研究，论文发表在 Invent. Math.，Adv. Math.，Trans. Amer. Math. Soc.，CMP 和 J. Algebra 等重要学术期刊上，标志性成果包括林-Nakano定理等，是国际上代数群、量子群、李代数及顶点算子代数等诸多领域研究中非常活跃且视野开阔的华人数学家。

欢迎各位参加！