Pseudo-derivations (-endomorphisms) of vertex algebras, and vertex bialgebras

报告人：李海生（美国Rutgers University-Camden）

时  间：2026年6月12日16:30

地  点：海韵园行政楼C503

内容摘要:

In the classical (Lie and associative) algebra theory, the notions of derivation and automorphism play a fundamental role. For any nonassociative algebra A, its derivations and automorphisms give (important examples of) a Lie algebra Der(A) and a group Aut(A), respectively. On the other hand, the universal enveloping algebras of Lie algebras and the group algebras form an important class of (cocommutative) Hopf/bialgebras.

In this talk, we shall discuss vertex-analogues of the notions of derivation,(end)automorphism, and bialgebra, which are called pseudo-derivation (due to Etingof-Kazhdan), pseudo-endomorphism, and vertex bialgebra. We present some basic results and give some applications. In particular, for any nonlocal vertex algebra V , we introduce a classical associative algebra B(V ) which contains all pseudo-derivations and pseudo-endomorphisms and prove that B (V ) is naturally a (nonlocal) vertex bialgebra if V is non-degenerate in the sense of Etingof-Kazhdan. Pseudo-derivation was used by Etingof-Kazhdan in their study of deformation quantization of vertex algebras, while pseudo-endomorphism was implicitly used before to construct simple current modules for vertex algebras and has been used in the deformation construction of quantum vertex algebras.

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