## 2019年度代數教學基層組織教學學術報告會

12月5日下午：

2:30-3:20: “從矩陣的相抵標准形談起

报告人：王卿文 教授（上海大学）；

3:30-4:20: “Drinfeld double of deformed quantum algebras”

报告人：樊赵兵 教授（哈尔滨工程大学）；

4:30-5:20: “表示代数的一些新趋势”

报告人：李立斌 教授（扬州大学）

12月6日下午：

1:30-2:20: “微积分的新思想”

報告人：張景中 院士（廣州大學）；

2:30-3:20: “大學數學啓蒙精彩案例

報告人：李尚志 教授（北京航空航天大學、國家級教學名師）；

3:30-4:20：“線性代數“金課”建設的思考與實踐”

報告人：陳建龍 教授（東南大學）；

4:30-5:20: 浙大對于中學與大學數學嵌接教學的思考與實踐
报告人：黄正达 教授（浙江大学）

Title: Drinfeld double of deformed quantum algebras
Abstract: We provide a deformation, f_{\alpha, \beta} , of Lusztig algebra f. Various quantum algebras in literature, including half parts of two-parameter quantum algebras, quantum superalgebras, and multi-parameter quantum algebras/superalgebras, are all specializations of f_{\alpha, \beta} . Moreover, f_{\alpha, \beta} is isomorphic to Lusztig algebra f up to a twist. As a consequence, half parts of those quantum algebras are isomorphic to Lusztig algebra f over a big enough ground field up to certain twists. We further construct the entire algebra U _{\beta, \xi} by Drinfeld double construction. As special cases, above quantum algebras all admit a Drinfeld double construction under certain assumptions. This is a joint work with Junjing Xing.

for the study of tensor category (such as the category of _nite dimensional repre-

sentations over group algebra, Lie algebra, Hopf algebra and quantum groups),

and has been proven useful in representation theory and other _elds. In this

talk, we will recall a little bit history and basic properties of representation ring

and representation algebra, and then report some new trends in representation

algebras of some classes of Hopf algebras and applications.