报告地点：行健楼学术活动室526
邀请人：周海燕教授
摘要：Let R be an artin algebra. Under certain Auslander-type conditions, we give some equivalent characterizations of (weakly) Gorenstein algebras in terms of the properties of Gorenstein projective modules and modules satisfying Auslander-type conditions. As applications, we provide some support for several homological conjectures. In particular, we prove that if R is left quasi Auslander, then R is Gorenstein if and only if it is (left and) right weakly Gorenstein; and that if R satisfies the Auslander condition, then R is Gorenstein if and only if it is left or right weakly Gorenstein. This is a reduction of an Auslander--Reiten's conjecture, which states that R is Gorenstein if $R$ satisfies the Auslander condition.
报告人简介：黄兆泳，南京大学数学系教授，博士生导师，主要从事同调代数和代数表示论的研究工作，曾获中国高校科学技术奖自然科学奖二等奖和江苏省数学杰出成就奖。主持国家自然科学基金面上项目多项，多次在国内外重要学术会议作大会报告，并多次应邀访问美国，日本和德国等多所著名高校，已在Israel J. Math.，Publ. RIMS，Forum Math.，J. Algebra，J. Pure Appl. Algebra等权威学术期刊发表论文120余篇。
