数学学科2020系列学术报告之七、八

理学院 2020-06-28 14:42:28

报告人:生云鹤,吉林大学,国家优秀青年基金获得者。

Title: Deformations of O-operators on Leibniz algebras and Leibniz bialgebras

时间:2020/7/1 14:30-15:30   地点:腾讯会议:

https://meeting.tencent.com/s/8uX6TujWDPGu

会议 ID:689 492 999

摘要:In this talk, we study (proto-, quasi-)twilled Leibniz algebras and the associated L-infty-algebras and differential graded Lie algebras. As applications, first we study   the twilled Leibniz algebra corresponding to the semidirect product of a Leibniz algebra and its representation. We show that O-operators  on this Leibniz algebra can be characterized as Maurer-Cartan elements of the associated gLa. Furthermore, an O-operator will give rise to a dgLa that can control its deformations. Then we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, quadratic twilled Leibniz algebras and Leibniz bialgebras are equivalent. We further define classical Leibniz-Yang-Baxter equation, classical Leibniz r-matrix and  triangular Leibniz bialgebra using  the associated gLa and the twisting theory of twilled Leibniz algebras. We introduce the notion of a Leibniz-dendriform algebra as the algebraic structure underlying an O-operator, by which we can construct  solutions  of the classical Leibniz-Yang-Baxter equation.

报告人简介:生云鹤,男,吉林大学数学学院教授、博士生导师、基础数学系主任。2004年6月毕业于吉林大学,获理学学士学位;2008年12月毕业于北京大学,获理学博士学位,2007年12月至2008年11月荷兰乌特列支大学数学系联合培养;2008年12月至2009年8月德国哥廷根大学博士后。主要研究领域为Poisson几何、非线性李理论、高阶李理论。在Comm. Math. Phys.、Int. Math. Res. Not. IMRN、Transform. Groups、J. Algebra、Pacific J. Math.等著名期刊发表学术论文50余篇。主持国家自然科学基金委优秀青年基金、面上项目等多项国家级和省部级项目。




报告人:陈良云,东北师范大学

题目:Derivations, Biderivations,triple derivations and  triple homomorphisms on Jordan algebras

时间:2020/7/1 15:30-16:30, 地点:腾讯会议

摘要:In this talk, we mainly study derivations, biderivations and triple derivations on Jordan algebras. Firstly, the sufficient and necessary conditions for their derivation algebras being simple are given. As an application, triple derivations of derivation algebras of semi-simple Jordan algebras are studied. Then we give a theorem about the relationship between biderivations and centroid of Jordan algebras and show that triple derivations are all derivations on Jordan algebras under some assumptions. Moreover, we also give a theorem about triple homomorphisms on Jordan algebras. This talk is a report on joint work with Yao Ma and Chenrui Yao.

报告人简介:  陈良云,东北师范大学数学与统计学院三级教授、博士生导师、博士后合作导师。南开大学理学博士、哈尔滨工业大学博士后、东京大学博士后。吉林省拔尖创新人才、吉林省教育厅新世纪优秀人才、长春市有突出贡献专家,省级精品课负责人。主要研究方向是李超代数及其应用,发表90余篇SCI论文。曾主持4项国家自然科学基金、4项省部级项目。指导博士和博士后20余人、硕士60余人,其中2名博士和3名硕士获吉林省优秀学位论文。担任《山东大学学报》(理学版)、《海南热带海洋学院学报》及6个外国期刊编委,国家自然科学基金委员会、万人计划领军人才、国家博士后基金同行评议专家,吉林省自然科学基金评审组专家。