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数学 学术报告
报??告??人:生云鹤教授 (吉林大学) 刘杰锋副教授(东北师范大学) 唐荣博士(吉林大学)
时????????间:2021年3月4日(周四)上午8:30-11:30
地????????点:线上,腾讯会议号:866462390
主办单位:应用数学系
联系人:郎红蕾
联系方式:13693322305

题目:Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and O-operators

摘要: First we introduce the notion of a twilled 3-Lie algebra, and construct an-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 O-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. 

报告人简介:

生云鹤,吉林大学教授,《数学进展》编委,吉林省第十六批享受政府津贴专家(省有突出贡献专家)。2009年1月博士毕业于北京大学,从事Poisson几何、高阶李理论与数学物理的研究,2019年获得国家自然科学基金委优秀青年基金项目,在CMP, IMRN, JNCG, JA等杂志上发表学术论文60余篇,被引用400余次。

 

题目:Noncommutative Poisson bialgebras

摘要:In this talk, we introduce the notion of a noncommutative Poisson bialgebra, and establish the equivalence between matched pairs, Manin triples and noncommutative Poisson bialgebras. Using quasi-representations and the corresponding cohomology theory of noncommutative Poisson algebras, we study coboundary noncommutative Poisson bialgebras which leads to the introduction of the Poisson Yang-Baxter equation. A skew-symmetric solution of the Poisson Yang-Baxter equation naturally gives a (coboundary) noncommutative Poisson bialgebra. Rota-Baxter operators, more generally O-operators on noncommutative Poisson algebras, and noncommutative pre-Poisson algebras are introduced, by which we construct skew-symmetric solutions of the Poisson Yang-Baxter equation in some special noncommutative Poisson algebras obtained from these structures.

报告人简介:

刘杰锋,东北师范大学副教授,2016年于吉林大学获得博士学位。从事Poisson几何与数学物理的研究,在J. Symplectic Geom., J. Noncommut. Geo., J. Algebra等杂志上发表多篇高水平论文。

 


题目:Relative Rota-Baxter operators and Leibniz bialgebras

摘要:In this talk, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras and Leibniz bialgebras are equivalent. Then we introduce the notion of a (relative) Rota-Baxter operator on a Leibniz algebra and construct the graded Lie algebra that characterizes relative Rota-Baxter operators as Maurer-Cartan elements. By these structures and the  twisting theory of twilled Leibniz algebras, we further define the classical Leibniz Yang-Baxter equation, classical Leibniz r-matrices and  triangular Leibniz bialgebras.

报告人简介:

唐荣,吉林大学师资博士后,2019年博士毕业于吉林大学。从事罗巴代数和代数结构形变理论方面的研究工作,在Comm. Math. Phys.,J. Algebra,J. Geom. Phys.,J. Algebra Appl.等杂志上发表论文多篇。

 

 

欢迎各位老师同学参加!

 


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