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学术报告:Bimodule monomorphism categories and RSS equivalences via cotilting modules

发布时间:2017年12月12日 浏览次数:发布者:mathky

报告人:张跃辉教授

上海交通大学数学系

报告题目:Bimodule monomorphism categories and RSS equivalences via cotilting modules

报告时间:2017年1220日下午3:00-4:00

报告地点:海韵行政楼B313

摘要:This talk is based on a joint work with B.L.Xiong and P.Zhang. The monomorphism category M(A, M, B) induced by a bimodule  $_AM_B$ is the subcategory of $\Lambda$-mod consisting of \left[\begin{smallmatrix} X\\ Y\end{smallmatrix}\right]_{\phi}$ such that $\phi: M\otimes_B Y\rightarrow X$ is a monic A-map, where $\Lambda=\left[\begin{smallmatrix}A&M\\0&B\end{smallmatrix}\right]$, and A, B are Artin algebras. In general, M(A, M, B) is not the monomorphism category induced by quivers. It could describe the Gorenstein-projective m-modules. This monomorphism category is a resolving subcategory of $\modcat{\Lambda}$ if and only if M_B is projective. In this case, it has enough injective objects and Auslander-Reiten sequences, and can be also described as the left perpendicular category of a unique basic cotilting $\Lambda$-module. If M satisfies the condition (IP) , then the stable category of M(A, M, B) admits a recollement of additive categories, which is in fact a recollement of singularity categories if M(A, M, B) is a Frobenius category. Ringel-Schmidmeier-Simson equivalence between M(A, M, B) and its dual is introduced. If M is an exchangeable  bimodule, then an RSS equivalence is given by a $\Lambda$-$\Lambda$ bimodule which is a two-sided cotilting $\Lambda$-module with a special property; and the Nakayama functor N_m gives an RSS equivalence if and only if both A and B are Frobenius algebras.

联系人:林亚南教授

 

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