报告时间：2021年5月12日, 10:00-11:00

报告地点：腾讯会议：227 881 667

报告人：姚裕丰教授（上海海事大学）

报告摘要：Let $(\mathfrak{g}, [p])$ be a restricted Lie algebra over an algebraically closed field of characteristic $p>0$. Then the inverse limits of higher reduced enveloping algebras $\{u_{\chi^s}(\mathfrak{g})\mid s\in\mathbb{N}\}$ with $\chi$ running over $\mathfrak{g}^*$ make representations of $\mathfrak{g}$ split into different blocks. In this talk, we study such an infinite-dimensional algebra $\mathscr{A}_{\chi}(\mathfrak{g}):= \underleftarrow {\text{lim}} U_{\chi^s}(\mathfrak{g})$ for a given $\chi\in\mathfrak{g}^*$. A module category equivalence is built between subcategories of $U(\mathfrak{g})-mod$ and $\mathscr{A}_{\chi}(\mathfrak{g})-mod$. In the case of reductive Lie algebras, (quasi) generalized baby Verma modules and their properties are described. Furthermore, the dimensions of projective covers of simple modules with characters of standard Levi form in the generalized $\chi$-reduced module category are precisely determined, and a higher reciprocity in the case of regular nilpotent is obtained. If time is permitted, we further talk about the theory of support variety of restricted Lie algebras. A conjecture on support varieties of baby Verma modules is proposed, and the progress of the conjecture is presented.This is a joint work with Yi-Yang Li and Bin Shu.

报告人简介：姚裕丰，2010年毕业于华东师范大学数学系获数学博士学位。随后赴上海海事大学工作，现任上海海事大学数学系教授。研究领域涉及模李代数、无限维李代数、上同调支柱簇、以及有限群概形表示的p-点理论等等。在主流数学杂志Forum Mathematicum, Mathematische Nachrichten, Journal of Algebra, Journal of Pure and Applied Algebra等正式发表论文四十多篇。自入职以来其研究受到上海市与国家自然科学基金的持续支持。

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邀请人：白占强, 董超平