报告题目 (Title)：Actions of monoidal categories and representations of Cartan type Lie algebras
报告人 (Speaker)：裴玉峰教授（上海师范大学）
报告时间 (Time)：2021年10月25日(周一)9:00-11:00
报告地点 (Place)：线上腾讯会议, 会议号：628 545 664
邀请人(Inviter)：张姣
报告摘要：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 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.