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Gorenstein homological properties and spectrum theory of category algebras
发布时间:2018-04-11     点击次数:
报告题目: Gorenstein homological properties and spectrum theory of category algebras
报 告 人: 汪任 博士(中国科技大学)
报告时间: 2018年04月19日 16:00--17:00
报告地点: 理学院东北楼四楼报告厅(404)
报告摘要:

 For a finite EI category, we prove that its category algebra is Gorenstein if and only if the given category is projective; and that its category algebra is 1-Gorenstein if and only if the given category is free and projective. For a finite projective EI category, the stable category of Gorenstein-projective modules over the category algebra is tensor triangle equivalent to the singularity category of the category algebra. If in addition the category is free, we construct a maximal Cohen-Macaulay approximation of the trivial module, which is exactly the tensor identity of the above stable category. In this case, we prove that Gorenstein-projective modules are closed under the tensor product if and only if each morphism in the given category is a monomorphism. We compute the spectrum in the sense of Balmer of the singularity category of a finite projective EI category algebra.

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