报告题目：幺半范畴和嘉当型李代数的表示
摘要：Using crossed homomorphisms, we show that the category of weak representations (resp. admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs) is an action of the monoidal category of representations of Lie algebras. In particular, the corresponding bifunctor is established to give new weak representations (resp. admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs). This generalizes and unifies various well-known constructions of representations of Cartan type Lie algebras by using this new bifunctor. We construct some crossed homomorphisms in different situations and use our actions of monoidal categories to recover some known constructions of representations of various Lie algebras, also to obtain new representations for generalized Witt algebras and their Lie subalgebras. The cohomology theory of crossed homomorphisms between Lie algebras is introduced and used to study linear deformations of crossed homomorphisms. This is a joint work with Yufeng Pei, Rong Tang and Kaiming Zhao.
时间：2021年10月18日，16:00-18:30
地点：腾讯会议(会议号: 614 608 632)
报告人: 生云鹤教授（吉林大学）
报告人简介：生云鹤，吉林大学教授， 2009年1月博士毕业于北京大学， 2019年获得国家自然科学基金委优秀青年基金项目，《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）。从事Poisson几何、高阶结构与数学物理的研究，在Comm. Math. Phys., Adv. Math. IMRN, J. Noncomm. Geom., J. Algebra等杂志上发表学术论文60余篇，被引用400余次。