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广州数学大讲坛第37期

刘杰锋副教授、唐荣博士学术报告

时间:2021-09-14 点击数:

东北师范大学刘杰锋副教授学术报告


题目:F-manifold algebras and deformation quantization via pre-Lie algebras

时间:2021.9.17(周五),14:30-15:30

地点:腾讯会议(会议ID:594483384)

报告人:刘杰锋副教授(东北师范大学)


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 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 on F-manifold algebras to construct pre-F-manifold algebras. This is a joint work with Chengming Bai and Yunhe Sheng.

报告人简介

刘杰锋,东北师范大学副教授,2016年博士毕业于吉林大学,从事Poisson几何与数学物理的研究,在J. Symplectic Geom., J. Noncommut. Geom., J. Algebra等杂志上发表多篇高水平论文。



吉林大学唐荣博士学术报告


题目:Homotopy Rota-Baxter operators and post-Lie algebras

时间:2021.9.17(周五),15:30-16:30

地点:腾讯会议(会议ID:594483384)

报告人:唐荣博士(吉林大学)

摘要:Rota-Baxter operators and the more general O-operators on Lie algebras together with their interconnected pre-Lie and post-Lie algebras are important algebraic structures with broad applications. This paper introduces the notions of a homotopy Rota-Baxter operator and a homotopy O-operator on a symmetric graded Lie algebra. Their characterization by Maurer-Cartan elements of suitable differential graded Lie algebras is provided. Through the action of a homotopy O-operator on a symmetric graded Lie algebra, we arrive at the notion of an operator homotopy post-Lie algebra, together with its characterization in terms of Maurer-Cartan elements. A cohomology theory of post-Lie algebras is established, with an application to 2-term skeletal operator homotopy post-Lie algebras.

报告人简介

唐荣,吉林大学师资博士后,2019年博士毕业于吉林大学,从事罗巴代数和代数结构形变理论方面的研究,在Comm. Math. Phys.,J. Algebra,J. Geom. Phys.等杂志上发表论文多篇。

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