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趣购彩代理学术讲述:Pairing and duality of algebraic quantum groupoids

公布日期: 2020-01-05阅读次数:

讲述问题:Paring and duality of algebraic quantum groupoids

讲述人:王栓宏传授(西北大学)

讲述工夫:2020年1月6日(周一)16:00

讲述地址:教四楼B411

择要: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)

 

讲述人简介:西北大学数学学院二级传授、博士生导师,获复旦大学博士学位,韩国全南国立大学博士后,比利时K.U.鲁汶大学博士后。河南省卓越青年迷信基金取得者。现任西北大学教务处副处长,江苏省初等学校数学讲授研讨会理事长。

次要研讨偏向为Hopf代数与部分紧量子群、数学物理方式、Hopf代数、辫子范围实际、量子群、李代数等。先后掌管完成国度天然迷信基金项目5项,省部级以上科研项目10多项。揭晓研讨性论文140余篇,此中SCI论文100余篇,讲授改造论文6篇,省教改项目4项,获江苏省科技提高奖三等2项。2018与2019年延续两次获西北大学“我最喜好的先生”十佳。