Lie-Cartan modules and cohomology for Lie algebras of polynomial vector fields

发布时间：2025-03-10 作者：浏览次数：

Speaker:	姚裕丰	DateTime:	2025年3月15日（周六）上午 10:00-11:00
Brief Introduction to Speaker: 姚裕丰教授主要研究兴趣为李代数表示以及相关的支柱簇/代数簇理论。数学研究活跃，成果丰富。自任职以来主持国家自然科学基金青年/面上项目，以及上海市科学创新项目/自然科学基金项目多项。		Place:	国交2号楼201
Abstract:In this talk, I introduce a category arising from the BGG category for Lie algebras of polynomial vector fields. The objects of this category are so-called Lie-Cartan modules which admit both Lie-module structure and compatible $R$-module structure where $R$ denotes the corresponding polynomial ring. We give the classification of simple Lie-Cartan modules. If time is permitted, I further introduce the cohomology theory for this category, extending the usual Chevalley-Eilenberg cohomology theory. For the case of Lie algebras of Witt type, the extension ring $\Ext^{\bullet}(R, R)$ for the polynomial algebra $R$ is isomorphic to the usual cohomology ring $H^{\bullet}(gl(n))$ of the general linear Lie algebra $gl(n)$, so that it is finite dimensional. This is a joint work with Feifei Duan and Bin Shu.