金融与数学金沙国际(唯一)官网学术报告预告

发布者:学术动态管理员发布时间:2019-05-09浏览次数:13

报告一:The Extension Dimensions of Abelian Categories

报 告 人:黄兆泳  南京大学教授,博导

报告时间:2019512日(周日)上午8:00

报告地点:金沙国际(唯一)官网B403

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,江苏省数学会杰出成就奖获得者,在表示论和同调理论方面做出了杰出的贡献,在《J. Algebra》、《J. Pure Appl. Algebra》等代数学顶级期刊上发表论文90余篇。2001年,获中国高校科学技术奖自然科学奖二等奖,2002年入选江苏省普通高校“青蓝工程”第二期首批优秀青年骨干金沙澳门官网培养人选。近年来,连续主持国家自然科学基金面上项目多项。

  

  

报告二: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:2019512日(周日)上午10:00

报告地点:金沙国际(唯一)官网B403

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 IwanagaGorenstein. 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.

报告人概况:张孝金,博士,南京信息工程大学数学与统计金沙国际(唯一)官网副教授,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。

 

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