报告题目：Loewy Filtration and Quantum de Rham Cohomology

报告时间：2015年7月17日  16：00 –17：00

报告地点：数学与统计学院 3楼 会议室310

报告人：华东师范大学  胡乃红 教授

报告摘要：This talk is about (1) the indecomposable submodule structures of quantum divided power algebra $\mathcal{A}_q(n)$ introduced by myself in 1999 and its truncated objects $\mathcal{A}_q(n,\bold m)$, where an ``intertwinedly-lifting" method is established to prove the indecomposability of a module when its socle is non-simple. (2) the Loewy filtrations are described for all homogeneous subspaces $\mathcal{A}^{(s)}_q(n)$ or $\mathcal{A}_q^{(s)}(n, \bold m)$, the Loewy layers and dimensions are determined. The rigidity of these indecomposable modules is proved. An interesting combinatorial identity is derived from our realization model for a class of indecomposable $\mathfrak{u}_q(\mathfrak{sl}_n)$-modules. (3) Meanwhile, the quantum Grassmann algebra $\Omega_q(n)$ over $\mathcal{A}_q(n)$ is constructed, together with the quantum de Rham complex $(\Omega_q(n), d^\bullet)$ via defining the appropriate$q$-differentials, and its subcomplex $(\Omega_q(n,\bold m), d^\bullet)$. For the latter, the corresponding quantum de Rham cohomology modules are decomposed into the direct sum of some sign-trivial modules.

报告人简介： 胡乃红，华东师范大学教授，博导，研究方向为李理论、量子群及其表示理论。 德国洪堡学者(95-96年度)，曾获第三届教育部《高校青年教师奖》，教育部第八届“霍英东青年教师奖”研究类二等奖；教育部首批“高校优秀骨干教师奖”。