题目:Generalized Shen-Larsson bifunctors and cohomologies of crossed homomorphisms

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 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.I will tell you the first Lie algebra who has a complete classification of simple weight modules, some of which have all infinite dimensional weight spaces.

赵开明，教授，博士生导师。1991年中国科学院博士毕业，先后在美国威斯康辛大学、加拿大滑特鲁大学等多所世界著名大学从事博士后研究，1999年入选中国科学院“百人计划”，现任加拿大罗瑞尔大学教授。主要从事李代数、非交换代数、结合代数、可除代数等领域的研究工作。在  Adv.Math., Selecta Math.，Proc. London Math.Soc，Math. Z.，Trans. Amer. Math. Soc.，Doc. Math.，Transform. Groups，J. Lond. Math. Soc.，Israel J. Math，J. Algebra等国际重要学术期刊上发表高水平学术论文100余篇。代表工作有：解决了广义Kac猜想；系统完整解决了Catan型李代数的结构问题；解决了经典Heisenberg-Virasoro李代数的不可约Harish-Chandra模的分类问题；给出了一大类Toroidal李超代数的可积单模的分类； 给出了在正交合同之下对称，反对称，及正交矩阵的三对角标准型；发现了一些具有较大自同构群的实可除代数等等。主持完成3项加拿大研究理事会基金项目、4项中国国家自然科学基金项目，是国际代数学领域有重要影响的专家。

2019-8-25上午9点

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