报告题目：Paring and duality of algebraic quantum groupoids

报告人：王栓宏教授（东南大学）

报告时间：2020年1月6日（周一）16：00

报告地点：教四楼B411

摘要：Algebraic quantum groupoids have been developed by two of the authors (AVD and SHW) of this note in a series of papers. Regular multiplier Hopf algebroids are obtained also by two authors (TT and AVD). Integral theory and duality for those have been studied by one author here (TT). Finally, again two authors of us (TT and AVD) have investigated the relation between weak multiplier Hopf algebras and multiplier Hopf algebroids. In the paper 'Weak multiplier Hopf algebras III. Integrals and duality' (by AVD and SHW), one of the main results is that the dual of an algebraic quantum groupoid, admits a dual of the same type. In the paper 'On duality of algebraic quantum groupoids' (by TT), a result of the same nature is obtained for regular multiplier Hopf algebroids with a single faithful integral. The duality of regular weak multiplier Hopf algebras with a single integral can be obtained from the duality of regular multiplier Hopf algebroids. That is however not the obvious way to obtain this result. It is more difficult and less natural than the direct way. We will discuss this statement further in the paper. Nevertheless, it is interesting to investigate the relation between the two approaches to duality in greater detail. This is what we do in this paper. We build further on the intimate relation between weak multiplier Hopf algebras and multiplier Hopf algebroids. We now add the presence of integrals. That seems to be done best in a framework of dual pairs. It is in fact more general than the duality of these objects coming with integrals. (joint work with T. Timmermann and A. Van Daele)

报告人简介：东南大学数学学院二级教授、博士生导师，获复旦大学博士学位，韩国全北国立大学博士后，比利时K.U.鲁汶大学博士后。河南省杰出青年科学基金获得者。现任东南大学教务处副处长，江苏省高等学校数学教学研究会理事长。

主要研究方向为Hopf代数与局部紧量子群、数学物理方法、Hopf代数、辫子范畴理论、量子群、李代数等。先后主持完成国家自然科学基金项目5项，省部级以上科研项目10多项。发表研究性论文140余篇，其中SCI论文100余篇，教学改革论文6篇，省教改项目4项，获江苏省科技进步奖三等2项。2018与2019年连续两次获东南大学“我最喜欢的老师”十佳。