加入收藏  || English Version 
 
2019代数学系列报告之六、七、八(张孝金&陈小伍&黄兆泳)

  发布日期:2019-05-06  浏览量:327


  

报告题目一:sTilting modules over Auslander Gorenstein algebras

报 告 人:张孝金(南京信息工程大学副教授)

报告时间:2019511日(周六)上午9:00-9:50

报告地点:磬苑校区理工H401

报告摘要:For a finite-dimensional algebra A and a nonnegative integer n, we characterize when the set tiltn A of

additive equivalence classes of tilting modules with projective dimension at most n has a minimal (or equivalently, minimum) element. This generalizes results of Happel and Unger. Moreover, for an n-Gorenstein algebra A with n>= 1, we construct a minimal element in tiltn A.  As a result, we give equivalent conditions for a k-Gorenstein algebra to be Iwanaga–Gorenstein. Moreover, for a 1-Gorenstein algebra A and its factor algebra B=A/(e), we show that there is a bijection between tilt1A and the set st-tilt B of additive equivalence classes of basic support tau-tilting B-modules, where e is an idempotent such that eA is the additive generator of the category of projective-injective A -modules.

专家概况:张孝金,博士,南京信息工程大学数学与统计学院副教授,主要研究领域为同调代数和代数表示论中的高维AR-理论和tau-倾斜理论。先后多次访问过德国的Bielefeld大学,日本的Nagoya大学等国际著名大学,主持国家自然科学基金青年项目1项,并参与多项国家自然科学基金的研究,已在Journal of Algebra, Science China Mathematics, Osaka Journal of Mathematics, Journal of Austrian Mathematical Society等数学国际知名杂志上发表论文10余篇。

  

  

报告题目二:Recollements, comma categories and morphic enhancements

报 告 人:陈小伍(中国科学技术大学教授,国家优秀青年基金获得者

报告时间:2019511日(周六)上午10:00-10:50

报告地点:磬苑校区理工H401

报告摘要:We relate a recollement of triangulated categories to a certain comma category. For a morphic enhancement in the sense of Keller, we obtain three functors, which relate the enhanced triangulated category to the module category over the given triangulated category. This extends the work by Ringel-Zhang (2014) and Eiriksson (2017).

专家概况:陈小伍,中国科学技术大学教授、博士生导师,曾获得德国洪堡奖学金、教育部新世纪优秀人才支撑计划以及中国博士后科学基金特别资助,2014年入选中国科学院“卓越青年科学家”项目;2015年获国家自然科学基金优秀青年科学基金。主要研究方向为代数表示理论、同调代数;其主要研究课题为代数的导出范畴、奇点范畴理论、Gorenstein环、Hopf代数与量子群等。已在国内外权威期刊Adv. Math.IMRNDoc. Math.Math. Z.以及 J. Algebra 等上发表论文50多篇论文。

  

  

 

报告题目三:The Extension Dimensions of Abelian Categories

报 告 人:黄兆泳(南京大学教授,博导)

报告时间:2019511日(周六)上午11:00-11:50

报告地点:磬苑校区理工H401

报告摘要:Let $\mathcal{A}$ be an abelian category having enough projective objects and enough injective objects. We prove that if $\mathcal{A}$ admits an additive generating object, then the extension dimension and the weak resolution dimension of $\mathcal{A}$ are identical, and they are at most the representation dimension of $\mathcal{A}$ minus two. By using it, for a right Morita ring $\Lambda$, we establish the relation between the extension dimension of the category mod-$\Lambda$ of finitely generated right $\Lambda$-modules and the representation dimension as well as the global dimension of $\Lambda$. In particular, we give an upper bound for the extension dimension of mod-$\Lambda$ in terms of the projective dimension of certain class of simple right $\Lambda$-modules and the radical layer length of $\Lambda$. In addition, we investigate the behavior of the extension dimension under some ring extensions.

报告人概况:黄兆泳,南京大学数学系教授,博士生导师,曾获中国高校科学技术奖自然科学奖二等奖,江苏省数学会杰出成就奖。在表示论和同调理论方面做出了杰出的贡献,多次应邀访问了美国、日本和德国的数所高校,近年来,黄兆泳教授连续主持国家自然科学基金面上项目多项,已在Isr. J. Math.J. AlgebraJ. Pure Appl. Algebra等代数学顶级期上刊发表论文90余篇。

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

打印此页】【顶部】【关闭
   
版权所有 2019 澳门赌搏网站大全 All rights reserved 皖ICP备05018241号
地址:安徽省合肥市九龙路111号澳门新莆京娱乐网站磬苑校区理工楼H楼 邮编:230601 E-mail:math@ahu.edu.cn
访问统计:自2013年9月1日以来总访问:1000  后台管理


XML 地图 | Sitemap 地图