报告题目：Braided Nijenhuis Jacobi-Jordan Bialgebras: Bosonisation, Transmutation, and Low-Dimensional Classifications

主讲人：马天水 教授（河南师范大学）

摘要：We investigate braided Nijenhuis Jacobi-Jordan bialgebras, where Jacobi-Jordan algebras are commutative algebras satisfying the Jacobi identity. Starting from Nijenhuis Jacobi-Jordan bialgebras and their (co)representations, we introduce a crossed module framework and formulate compatibility conditions for braided bialgebra structures. We study the bosonisation construction, which combines a braided bialgebra with its base bialgebra, and a transmutation construction associated with bialgebra morphisms. In the quasitriangular setting, we describe induced crossed modules and examine finite-dimensional duality and the factorisable case. To complement these structural results, we present low-dimensional Jacobi-Jordan bialgebra structures in dimensions two, three, and four, discuss Nijenhuis operators in these settings, and give explicit examples of braided Nijenhuis Jacobi-Jordan bialgebras. The results connect structural constructions with concrete classifications in the commutative Jacobi-type setting.

报告时间：2026年11月5日下午 15:00 - 15:50

报告地点：国产自拍 301室

报告人简介：马天水，河南师范大学数学与信息科学学院教授、河南省高等学校骨干教师、河南省一流本科课程《线性代数》负责人。 主要从事Hopf代数理论的相关研究，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。