报告题目：Nijenhuis operators and pre-Lie algebras

主讲人：马天水 教授（河南师范大学）

摘要：Pre-Lie bialgebras (or left-symmetric bialgebras) were introduced by Bai as an analogue of Lie bialgebras. Nijenhuis operator on a pre-Lie algebra was introduced by Wang et al, which can generate a trivial deformation. In this talk, we present a method to construct Nijenhuis operators on pre-Lie algebras based on a class of pre-Lie bialgebras, which provides a motivation to study Nijenhuis pre-Lie algebras. On the other hand, we introduce Nijenhuis operators on pre-Lie coalgebras and at the same time give a construction. Then we investigate the bialgebraic structures on Nijenhuis pre-Lie algebras by using dual representations. We also give the classification of symplectic pre-Lie algebras and quasitriangular pre-Lie bialgebras of dimension 2.

报告时间：2025年5月23日上午08:30 - 09:30

报告地点：新葡萄8883官网AMG301室

报告人简介：

马天水，东南大学理学博士，东北师范大学博士后，瑞典梅拉达伦大学博士后。现为河南师范大学数学与统计学院教授、博士生导师、河南省一流本科课程《线性代数》负责人。主要从事Hopf代数及其应用的相关研究，在Asian J. Math、J. Algebra、Algebr. Represent. Theory等SCI收录杂志发表论文50余篇。主持在研或完成国家自然科学基金面上项目、青年项目和欧盟FUSION 项目、河南省自然科学基金面上项目、中国博士后基金面上项目等。曾获河南省高等学校青年骨干教师、河南省优秀硕士毕业论文指导教师等荣誉称号。