2019代数学系列报告之六（张孝金副教授）
报告题目： 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：2019年5月11日（周六）上午9:00-9:50
报告地点：磬苑校区理工H楼401室
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) elem
-ent. 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.
2019年代数学系列讲座之七（陈小伍教授）
报告题目：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：2019年5月11日（周六）上午10:00-10:50
报告地点：磬苑校区理工H楼401室
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).
2019代数学系列讲座之八（黄兆泳教授）
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11日（周六）上午11:00-11:50
报告地点：磬苑校区理工H楼401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.
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科学技术处
2019年5月7日