報 告 人：姜軍 博士

報告題目：Deformation maps of quasi-twilled Lie algebras   

報告時間：2024年8月12日（周一）下午16：20

報告地點：靜遠樓1508學術報告廳

主辦單位：數(shù)學與統(tǒng)計學院、數(shù)學研究院、科學技術研究院 

報告人簡介：

      姜軍博士，2023年博士畢業(yè)于吉林大學，主要研究方向為李理論與Rota-Baxter李群等，在李代數(shù)的上同調和形變理論等方面取得了一系列研究成果，在J. Lond. Math. Soc., J. Noncommut. Geom., J. Algebra等高水平雜志發(fā)表學術論文多篇。

報告摘要： 

       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.