报告题目 (Title)：Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2
（特征2域上的左对称超代数与李超代数的拉格朗日扩张）
报告人 (Speaker)：Sofiane Bouarroudj(纽约大学阿布扎比分校)
报告时间 (Time)：2025年10月22日 (周三) 15:30-16:30
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：张红莲教授
主办部门：理学院数学系
报告摘要：
The purpose of this talk is twofold. First, we introduce the notions of left-symmetric and left alternative structures on superspaces in characteristic 2. We describe their main properties and classify them in dimension 2.
Secondly, we present a method of Lagrangian extension of Lie superalgebras in characteristic 2 with a flat torsion-free connection. We show that any strongly polarized quasi-Frobenius Lie superalgebra can be obtained as a Lagrangian extension. Further, we demonstrate that Lagrangian extensions are classified by a certain cohomology space that we introduce. To illustrate our constructions, all Lagrangian extensions in dimension 4 have been described. This is a joint work with S. Benayadi and Q. Ehret.
