报告题目：Actions of monoidal categories and crossed homomorphisms

报 告 人：裴玉峰教授 上海师范学院

报告时间：2020年6月4日 14:00-15:00

报告地点：腾讯会议 会议 ID：978 473 727

校内联系人：唐荣 tangrong@jlu.edu.cn

报告摘要：

In this talk, using crossed homomorphisms, we show that the category of weak representations (resp. admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs) is a left module category over the monoidal category of representations of Lie algebras. In particular, the corresponding bifunctor which we call the action of monoidal categories is established to give new weak representations (resp. admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs). This generalizes and unifies various existing constructions of representations of many 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.

报告人简介：

裴玉峰，上海师范大学教授。近年来主持完成国家自然科学基金面上项目1项、上海自然科学基金项目2项. 已经在《J.Algebra》、《Comm. Contem.Math.》、《J. Math. Phys.》等国际期刊上发表SCI收录论文30多篇。