报 告 人：姜军 博士
报告题目：Deformation maps of quasi-twilled Lie algebras
报告时间：2024年8月12日（周一）下午16：20
报告地点：静远楼1508学术报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
姜军博士，2023年博士毕业于吉林大学，主要研究方向为李理论与Rota-Baxter李群等，在李代数的上同调和形变理论等方面取得了一系列研究成果，在J. Lond. Math. Soc., J. Noncommut. Geom., J. Algebra等高水平杂志发表学术论文多篇。
报告摘要：
In this talk, we provide a unified approach to study the cohomology theories and deformation theories of various types of operators in the category of Lie algebras, including modified r-matrices, crossed homomorphisms, derivations, homomorphisms, relative Rota-Baxter operators, twisted Rota-Baxter operators, Reynolds operators and deformation maps of matched pairs of Lie algebras. The main ingredients are quasi-twilled Lie algebras. We further give the controlling algebras and cohomologies of deformation maps, which not only recover the existing results for crossed homomorphisms, derivations, homomorphisms, relative Rota-Baxter operators, twisted Rota-Baxter operators and Reynolds operators, but also leads to some new results which are unable to solve before, e.g. the controlling algebras and cohomologies of deformation maps of matched pairs of Lie algebras. This is a joint work with Yunhe Sheng and Rong Tang.