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Braided Lie Algebras, Double Biproducts and A Schur's Double Centralizer Theorem
澳门新葡8455最新网站:2019年12月16日 15:13 点击数:

报告人:王栓宏

报告地点:澳门新葡8455最新网站317室

报告澳门新葡8455最新网站:报告澳门新葡8455最新网站 2019年12月19日星期四14:30-15:15

邀请人:陈良云

报告摘要:

Let $H$ be a quasitriangular Hopf algebra and $B$ a coquasitriangular Hopf algebra. We construct a braided Lie algebra in ${}_H^B{\cal L}$(see [16]) by sketching this procedure in the framework of a braided Lie algebra concerning an algebra in any symmetric braided monoidal category ${\cal C}$, and study the structure of braided Lie algebras in ${}_H^B{\cal L}$, and in particular the braided Lie structure of an algebra $A$ in ${}_H^B{\cal L}$. Next, we study braided enveloping algebra of a braided Lie algebra in ${}_H^B{\cal L}$ by imitating the standard algebraic constructions. One of our results gives a positive answer to a question of [3, p.42]. Finally, we introduce a double biproduct which transforms braided Hopf algebras in ${}_H^B{\cal L}$ to usual Hopf algebra, and study its coalgebra structures. As application, using double biproduct and the above we unify and extend both Cohen-Fischman-Westreich-Schur's double centralizer theorem [5] and Fischman-Montgomery-Schur's double centralizer theorem [9] to the one for the generalized Long module category ${}_H^B{\cal L}$.

主讲人概况:

王栓宏,东南大学数学新葡京最新官网二级教授、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。

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