報告題目：Actions of monoidal categories and crossed homomorphisms
報 告 人：裴玉峰教授 上海師範學院
報告時間：2020年6月4日 14:00-15:00
報告地點：騰訊會議 會議 ID：978 473 727
校内聯系人：唐榮 tangrong@jlu.edu.cn
報告摘要：
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.
報告人簡介：
裴玉峰，上海師範大學教授。近年來主持完成國家自然科學基金面上項目1項、上海自然科學基金項目2項. 已經在《J.Algebra》、《Comm. Contem.Math.》、《J. Math. Phys.》等國際期刊上發表SCI收錄論文30多篇。
