裴玉峰，上海师范大学教授，主要从事无限维代数和数学物理的研究，在Commun. Contemp. Math.、J. Algebra、J. Math. Phys.等SCI期刊发表论文30多篇。近年来主持完成国家自然科学基金面上项目1项、青年项目1项、上海自然科学基金项目2项。
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-know 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. This is a joint work with Yunhe Sheng, Rong Tang and Kaiming Zhao.