主持人：周国栋 副教授
时间：2020年12月3日 10:00
地点：腾讯会议号：486654161

报告摘要:
The notion of an F-manifold algebra is the underlying algebraic structure of an F-manifold. We introduce the notion of pre-Lie formal deformations of commutative associative algebras and show that F-manifold algebras are the corresponding semi-classical limits. We study pre-Lie infinitesimal deformations and extension of pre-Lie n-deformation to pre-Lie (n+1)-deformation of a commutative associative algebra through the cohomology groups of pre-Lie algebras. We introduce the notions of pre-F-manifold algebras and dual pre-F-manifold algebras, and show that a pre-F-manifold algebra gives rise to an F-manifold algebra through the sub-adjacent associative algebra and the sub-adjacent Lie algebra. We use Rota-Baxter operators, more generally O-operators and average operators on F-manifold algebras to construct pre-F-manifold algebras and dual pre-F-manifold algebras.
报告人简介:
刘杰锋，博士，东北师范大学副教授，硕士生导师， 于2016年6月在吉林大学获得博士学位， 导师生云鹤教授。主要从事Poisson几何与高阶李理论的研究。现阶段关心可积系统背后的代数结构、李2-代数胚与同伦Poisson代数和四维拓扑场论相关的问题。在J. Symplectic Geom., J. Noncommut. Geom., J. Algebra等国际期刊上发表论文十余篇。现主持国家自然科学基金青年基金1项。