报告题目：The Extension Dimensions of Abelian Categories

报告人：黄兆泳（南京大学教授，博导）

报告时间：2019年5月12日（周日）上午8:00

报告地点：皖西学院B楼403室

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.

报告人简介：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教师培养人选。近年来，连续主持国家自然科学基金面上项目多项。