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      數學 學術報告
      報??告??人:生云鶴教授 (吉林大學) 劉杰鋒副教授(東北師范大學) 唐榮博士(吉林大學)
      時????????間:2021年3月4日(周四)上午8:30-11:30
      地????????點:線上,騰訊會議號:866462390
      主辦單位:應用數學系
      聯系人:郎紅蕾
      聯系方式:13693322305

      題目: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. 

      報告人簡介:

      生云鶴,吉林大學教授,《數學進展》編委,吉林省第十六批享受政府津貼專家(省有突出貢獻專家)。2009年1月博士畢業于北京大學,從事Poisson幾何、高階李理論與數學物理的研究,2019年獲得國家自然科學基金委優秀青年基金項目,在CMP, IMRN, JNCG, JA等雜志上發表學術論文60余篇,被引用400余次。

       

      題目: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.

      報告人簡介:

      劉杰鋒,東北師范大學副教授,2016年于吉林大學獲得博士學位。從事Poisson幾何與數學物理的研究,在J. Symplectic Geom., J. Noncommut. Geo., J. Algebra等雜志上發表多篇高水平論文。

       


      題目: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.

      報告人簡介:

      唐榮,吉林大學師資博士后,2019年博士畢業于吉林大學。從事羅巴代數和代數結構形變理論方面的研究工作,在Comm. Math. Phys.,J. Algebra,J. Geom. Phys.,J. Algebra Appl.等雜志上發表論文多篇。

       

       

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