報(bào)告題目：Auslander-type conditions and weakly Gorenstein algebras
報(bào)告人：黃兆泳 教授 南京大學(xué)
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邀請(qǐng)人：楊丹丹 李歡歡
報(bào)告時(shí)間：2025年4月27日（周日） 16：30
報(bào)告地點(diǎn)：南校區(qū)會(huì)議中心113會(huì)議室
報(bào)告人簡(jiǎn)介：黃兆泳，南京大學(xué)數(shù)學(xué)學(xué)院教授，博士生導(dǎo)師，主要從事同調(diào)代數(shù)和代數(shù)表示論的研究工作，曾獲中國(guó)高校科學(xué)技術(shù)獎(jiǎng)自然科學(xué)獎(jiǎng)二等獎(jiǎng)（2次）和江蘇省數(shù)學(xué)杰出成就獎(jiǎng)。主持國(guó)家自然科學(xué)基金面上項(xiàng)目多項(xiàng)，多次在國(guó)內(nèi)外重要學(xué)術(shù)會(huì)議作大會(huì)報(bào)告，并多次應(yīng)邀訪問(wèn)美國(guó)，日本和德國(guó)等多所著名高校，已在Israel J. Math.，Publ. RIMS，F(xiàn)orum Math.，Bull. London Math. Soc.和J. Algebra等權(quán)威學(xué)術(shù)期刊發(fā)表論文120余篇。
報(bào)告摘要：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.
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
