Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and O-operators
报告人：生云鹤
报告地点：数学与统计学院104室
报告时间：2021年6月21日星期一10:00-11:00
邀请人：陈良云
报告摘要：
First we introduce the notion of a twilled 3-Lie algebra, and construct an $L_\infty$-algebra, whose Maurer-Cartan elements give rise to new twilled 3-Lie algebras by twisting. In particular, we recover the Lie $3$-algebra whose Maurer-Cartan elements are $\huaO$-operators (also called relative Rota-Baxter operators) on 3-Lie algebras. Then we introduce the notion of generalized matched pairs of 3-Lie algebras using generalized representations of 3-Lie algebras, which will give rise to twilled 3-Lie algebras. The usual matched pairs of 3-Lie algebras correspond to a special class of twilled 3-Lie algebras, which we call strict twilled 3-Lie algebras. Finally, we use O-operators to construct explicit twilled 3-Lie algebras, and explain why an r-matrix for a 3-Lie algebra can not give rise to a double construction 3-Lie bialgebra. Examples of twilled 3-Lie algebras are given to illustrate the various interesting phenomenon.
主讲人简介：
生云鹤，吉林大学数学学院副院长，教授、博士生导师，吉林省政府津贴专家（省有突出贡献专家）。主要研究领域为Poisson几何、非线性李理论、高阶李理论与数学物理等。在《Adv. Math.》、《Comm. Math. Phys.》、《Int. Math. Res. Not. IMRN》、《J. Noncommut. Geom.》、《J. Algebra》、《Pacific J. Math.》等著名期刊发表学术论文60余篇。主持国家自然科学优秀青年基金、面上项目、青年项目、天元项目以及博士后基金项目等多项，并担任《数学进展》、《J. Nonlinear Math. Phys.》的杂志编委。
学校主页