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

Speaker：Haisheng Li (Rutgers University-Camden)

Time：2026-6-12 16:30

Location：Conference Room C503 at Administration Building at Haiyun Campus

Abstract:

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.