报告时间：2021年4月12日, 10:00-11:00

报告地点：腾讯会议：580 458 468

报告人：生云鹤 教授（吉林大学）

报告摘要：Rota-Baxter operators were originally defined on a commutative associative algebra by Rota. Then it was defined on Lie algebras as the operator form of the classical Yang-Baxter equation. Kupershmidt introduced a more general notion called O-operator (later called relative Rota-Baxter operator) for arbitrary representation. Rota-Baxter operators have fruitful applications in mathematical physics. We determine the L-infty-algebra that characterizes relative Rota-Baxter Lie algebras as Maurer-Cartan elements. As applications, first we determine the L-infty-algebra that controls deformations of a relative Rota-Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling deformations of the underlying Lie algebra and representation by the dg Lie algebra controlling deformations of the relative Rota-Baxter operator. Then we define the  cohomology  of relative Rota-Baxter Lie algebras and relate it to their infinitesimal deformations.  In particular the cohomolgoy of Rota-Baxter Lie algebras and triangular Lie bialgebras are given. Finally we introduce the notion of homotopy relative Rota-Baxter operators and show that the underlying structure is pre-Lie-infinity algebras. This talk is based on joint works with Chenming Bai, Li Guo, Andrey Lazarev and Rong Tang.

报告人简介：生云鹤，吉林大学教授，《数学进展》、《J. Nonlinear Math. Phys.》编委，吉林省第十六批享受政府津贴专家（省有突出贡献专家）。2009年1月博士毕业于北京大学，从事Poisson几何、高阶李理论与数学物理的研究，2019年获得国家自然科学基金委优秀青年基金项目，在CMP, IMRN,JNCG,JA等杂志上发表学术论文60余篇，被引用400余次。

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