Pseudo-derivations (-endomorphisms) of
vertex algebras, and vertex bialgebras
报告专家：李海生 教授（罗格斯大学）
报告时间：6月16日（周二）9:00-10:00
报告地点：国家天元数学西南中心516
报告摘要：
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 simplecurrent modules for vertex algebras and has been used in the deformation construction of quantum vertex algebras.
专家简介：
李海生，美国罗格斯大学肯顿分校终身教授，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等国际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）。
邀请人：任丽
