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Generalized Shen-Larsson bifunctors and cohomologies of crossed homomorphisms
澳门新葡8455最新网站:2019年08月29日 19:19 点击数:

报告人:裴玉峰

报告地点:澳门新葡8455最新网站317室

报告澳门新葡8455最新网站:2019年08月30日星期五14:40-15:20

邀请人:陈良云

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 which we call the generalized Shen-Larsson bifunctor 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 conceptually to evolve into one bifunctor. We construct some crossed homomorphisms in different situations and use our generalized Shen-Larsson bifunctors 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 Yunhe Sheng, Rong Tang, and Kaiming Zhao.

主讲人概况:

裴玉峰,上海师范大学教授。博士毕业于华东师范大学,先后于加拿大劳瑞尔大学、美国罗格斯大学做访问学者。主要从事顶点代数,无限维李代数,量子代数的结构和表示的工作,目前在Journal of Algebra 和Proceedings of AMS等杂志发表学术论文多篇,并主持国家自然科学基金面上项目。

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