报告题目：Abelian extensions、higher derivations and relative Rota-Baxter operators on Lie triple system
报告人：陈良云
报告时间：10月12日 9：00-10：00
报告地点：勤园21-306，腾讯会议：498 644 718
报告摘要： In this talk, we will introduce abelian extensions、higher derivations and relative
Rota-Baxter operators on Lie triple system. we first construct the thirdorder cohomology classes
by derivations of Lie triple system $A$ and Lie triple system $\mathfrak{L},$ obtain a Lie algebra
$G_{\theta_A}$ with a representation $\Phi$ on $H^3(\mathfrak{L},A),$ where $\theta_A$ is given
by an abelian extension. We study obstruction classes for extensibility of derivations of $A$ and
$\mathfrak{L}$ to those of $\tilde{\mathfrak{L}}.$ Furthermore, we study Lie triple systems with
higher derivations (LtsHDer pairs for short), and define the cohomology of LtsHDer pairs with
coefficients in modules. We also study its central extension, and prove that their isomorphism class is
determined by the third cohomology group of coefficients in trivial representation. The definition of
deformation of LtsHDer pairs is given, and its 1-parameter deformation is a 3-cocycle in cohomology
with specific coefficients. Finally, the Nijenhuis operators of LtsHDer pairs are discussed. Finally,
we introduce the notion of a relative Rota-Baxter operator of weight $\lambda$ on a Lie triple system
with respect to an action on another Lie triple system, which can be characterized by the graph of their
semidirect product. We also establish a cohomology theory for a relative Rota-Baxter operator of
weight $\lambda$ on Lie triple systems and use the first cohomology group to classify infinitesimal
deformations. These are the joint works with Yao Ma and Xueru Wu.
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，主持国家自然科学基金科研项目五项、省部级科研项目六项，主研国家面上项目三项，发表110余篇SCI论文，专著一部（科学出版社）。指导博士和博士后30余名，硕士80余名，有2名博士和4名硕士获省优秀毕业论文奖。担任《山东大学学报》(理学版)《海南热带海洋学院学报》和8个外刊编委，国家重点研发计划“数学和应用研究”重点专项评审组专家、吉林省自然科学基金评审组专家。