报告题目：Cohomologies, extensions and deformations of Leibniz Triple Systems
报 告 人：陈良云 教授 东北师范大学
报告时间：2021年10月14日 9:30-10:30
报告地点：腾讯会议ID：330 119 626
校内联系人：唐荣 tangrong@jlu.edu.cn
报告摘要：In this talk, we introduce the first and third cohomology groups of Leibniz triple systems, which can be applied to extension theory and $1$-parameter formal deformation theory. Specifically, we investigate the central extension theory for Leibniz triple systems and show that there is a one-to-one correspondence between equivalent classes of central extensions of Leibniz triple systems and the third cohomology group. We study the $T^*$-extension of a Leibniz triple system and we determined that every even-dimensional quadratic Leibniz triple system $(\mathfrak{L},B)$ is isomorphic to a $T^*$-extension of a Leibniz triple system under a suitable condition. We also develop the $1$-parameter formal deformation theory of Leibniz triple systems and prove that it is governed by the cohomology groups. Then, we introduce the notion of a LeibtsDer pair, i.e., a Leibniz triple system with a derivation. We define a representation of a LeibtsDer pair and the corresponding cohomologies. We prove that a LeibtsDer pair is rigid if the $H^3_D(\mathfrak{L},\mathfrak{L})=0.$ The central extensions of a LeibtsDer pair can be classified by the third cohomology group. For a pair of derivation, we construct third cohomology classes by using derivations of $\mathfrak{T}$ and $\mathfrak{L},$ then one obtain a Lie algebra $G_{\mathfrak{T}}$ with a representation $\Phi$ on $H^3(\mathfrak{L}, \mathfrak{T}).$ 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，曾主持国家自然科学基金4项和省部级项目5项，发表100余篇SCI论文。目前，指导博士和博士后30名，硕士70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)和《海南热带海洋学院学报》及7个外刊编委。
