学术报告报告题目：Basic structural results of the Yangians of type A.
报 告人：Alexander Molev教授（澳大利亚悉尼大学）
报告时间：2021年12月25日（星期六）上午10：00--11:00
报告地点：Zoom会议:889 2752 1892 (https://uni-sydney.zoom.us/j/88927521892)
或者Zoom国际号：https://uni-sydney.zoom.us/u/kbLqtgtHzp
邀 请人：刘明讲师 景乃桓教授
欢迎广大师生前往！
数学学院
2021年12月21日
报告摘要：The Yangians form a remarkable family of quantum groups related to rational solutions of the classical Yang--Baxter equation. For each simple finite-dimensional Lie algebra a over the field of complex numbers, the corresponding Yangian Y(a) is a canonical deformation of the universal enveloping algebra U(a[x]) for the polynomial current Lie algebra a[x]. Importantly, the deformation is considered in the class of Hopf algebras which guarantees its uniqueness under some natural `homogeneity' conditions. The representation theory of the Yangians Y(a) is a very much nontrivial and fascinating area. Although the finite-dimensional irreducible representations of Y(a) are classified, their general structure remains largely unknown. The goal of the course is to give an introduction to the Yangian structure theory and their representations. The Yangians associated with the simple Lie algebras of type A will be in our focus, as they are understood better than the Yangians of the remaining types and because many of their properties manifest in the general theory.Some acquaintance with the basics of Lie algebra theory will be assumed. This is the second lecture on Yangians and their representations. It will be focused on the algebra structures of the Yangian in type A.
报告人简介：Molev是悉尼大学教授，澳大利亚科学院院士，国际著名表示论专家，在Yangian 代数、组合数学等诸多研究领域都作出了重要的贡献。Molev教授2001年获得澳大利亚数学会奖，著有Yangian代数的权威名著。