报告时间：12月22日周一下午15:00-16:00
报告地点：数学楼401报告厅
报告人：张红莲
主持人：胡乃红
报告人简介：
张红莲，上海大学理学院数学系主任、教授，博士生导师，中国数学会十四届理事。曾任国家自然科学基金委数理学部流动项目主任。获上海市东方英才拔尖计划，全国优秀博士学位论文提名奖、上海市优秀博士学位论文、美国数学会Fan氏交流奖。上海市三八红旗集体（负责人）、上海市重点课程负责人、上海市教育系统三八红旗集体负责人、国家一流课程骨干成员（排名第二）。主要从事李理论、量子群、量子代数及其表示理论的研究。发表SCI论文34篇，其中代表作发表在Comm. Math. Phys.、Trans. Amer.Math. Soc.、SIGMA, J. Algebra、JPAA等期刊上。主持6项国家自然科学基金。
报告摘要：
In this talk, we establish the first rigorous framework for the Drinfeld super Yangian associated with an exceptional Lie superalgebra, which lacks a classical Lie algebraic counterpart. Specifically, we systematically investigate the Drinfeld presentation and structural properties of the super Yangian associated with the exceptional Lie superalgebra $D(2,1;\lambda)$. First, we introduce a Drinfeld presentation for the super Yangian associated with the exceptional Lie superalgebra $D(2,1;\lambda)$, explicitly constructing its current generators and defining relations. A key innovation is the construction of a PBW basis using degeneration techniques from the corresponding quantum loop superalgebra. Furthermore, we demonstrate that the super Yangian possesses a Hopf superalgebra structure, explicitly providing the coproduct, counit, and antipode. This talk is based on the joint work with Hongda Lin.