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Quantum supersymmetries and two quantum de Rham super complexes

发布时间:2024-12-31 作者: 浏览次数:
Speaker: 胡乃红 DateTime: 2025年1月3日(周五)16:00-17:00
Brief Introduction to Speaker:

胡乃红,华东师范大学数学学院教授、博导,华东师范大学中法基础数学联合实验室LIA执行主任,德国洪堡学者,从事李理论、量子群及Hopf代数结构与表示论研究。现任SCI杂志Frontiers of Mathematics编委。曾获得教育部霍英东青年教师奖(研究类)二等奖,第三届教育部优秀教师教学科研奖励计划暨教育部青年教师奖(部优青),上海市启明星计划和追踪计划。多次主持国家自然科学基金面上项目,教育部博士点基金项目,两次参与国家自然科学基金重点项目,并与美国北卡州立大学景乃桓教授合作获得杰出青年基金B类。在Crelle J.、Comm. Math. Phys.、Israel J. Math.、J. Algebra、J. Pure Appl. Algebra、Pacific J. Math国际著名学术刊物发表论文70余篇。

Place: 国交2号楼315
Abstract:In order to study the ``modular" representation theory of quantum gl(m|n) at root of unity, we introduce the quantum Manin supersapce and quantum (dual) Grassmann superalgebra with quantum divided power structure, and develop a kind of quantum differential calculus over them, and construct two kinds of quantum de Rham super complexes: one is of infinite length which is the quantized version of the classical analogue due to Manin-Deligne-Morgan in their early study of supermanifolds from gauge field theory, another is of finite length which has no classical analogue to our knowledge. For the latter, we prove the Poincare lemma for nontruncated complex, while for the truncated case, in order to calculate all the qauntum de Rham cohomologies we need to develop a specific technique to overcome the complicated difficulties encountered in the quantum supercase. This talk is based on a series of our joint work with Dr. Ge Feng, and Prof. Marc Rosso.