Determining cocommutative vertex bialgebras

：李海生（美国罗格斯大学）
：2024-05-17 08:00
：海韵园实验楼105报告厅

报告人：李海生（美国罗格斯大学）

时  间：2024年5月17日8:00

地  点：海韵园实验楼105报告厅

内容摘要:

This talk is about the structure of cocommutative vertex bialgebras. For a general vertex bialgebra $V$, we show that the set $G(V)$ of group-like elements is an abelian semigroup, whereas the set $P(V)$ of primitive elements is a vertex Lie algebra. For $g\in G(V)$, denote by $V_g$ the connected component containing $g$. Among the main results, we show that if $V$ is a cocommutative vertex bialgebra, then $V = \oplus_{g\in G(V)}V_g$, where $V_{\bf 1}$ is a vertex subbialgebra which is isomorphic to the vertex bialgebra $\mathcal{V}_{P(V)}$ associated to the vertex Lie algebra $P(V)$, and $V_g$ is a $V_{\bf 1}$-module for $g\in G(V)$. In particular, this shows that every cocommutative connected vertex bialgebra $V$ is isomorphic to $\mathcal{V}_{P(V)}$ and hence establishes the equivalence between the category of cocommutative connected vertex bialgebras and the category of vertex Lie algebras. Furthermore, under the condition that $G(V)$ is a group and lies in the center of $V$, we prove that $V = \mathcal{V}_{P(V)}\otimes\C[G(V)]$ as a coalgebra where the vertex algebra structure is explicitly determined. This talk is based on a joint work with Jianzhi Han and Yukun Xiao.  

个人简介：

Professor Haisheng Li, his main research is on vertex operator algebras and quantum vertex algebras. Among the main results are conceptual constructions of vertex algebras and their modules, twisted modules; A theory of quasi modules; A theory of (weak) quantum vertex algebras and $\phi$-coordinated modules; A conceptual association of double Yangians and quantum affine algebras with quantum vertex algebras.

 

联系人：王清