报告人：周潘岳 教授
报告题目：Auslander--Reiten relations and local finiteness in extriangulated categories
报告时间：2026年11月7日14:50-15:30
报告地点：云龙校区智华楼201报告厅
报告人简介：
周潘岳，长沙理工大学数学与统计学院教授，博士生导师，湖南省数学学会理事，湖南省青年骨干教师，清华大学博士后，加拿大University of Sherbrooke博士后，主要从事代数表示论与同调理论的研究。先后主持国家自然科学基金面上项目和青年项目各1项以及省部级科研项目3项。研究成果发表在Science China Mathematics，Canadian Journal of Mathematics，Proceedings of the Royal Society of Edinburgh Section A: Mathematics，Pacific Journal of Mathematics，Journal of Algebra，Journal of Pure and Applied Algebra，Algebras and Representation Theory等国际知名学术期刊上。
报告摘要：
Let C be a Hom-finite Krull-Schmidt extriangulated category over a commutative artin ring. Write Rel(C) for the subgroup of the split Grothendieck group generated by the relations of all E-triangles, and AR(C) for the subgroup generated by those coming from Auslander--Reiten E-triangles. We first prove that either one-sided finiteness condition on Hom supports implies Rel(C) = AR(C). For incoming Hom supports, the proof uses a Jordan--Holder filtration of the contravariant defect. The outgoing case follows by duality. This gives a new proof of the implication from local finiteness to generation by Auslander-Reiten relations. Our argument uses defects and induction on their composition length. In this way, it avoids the radical filtration argument used by Zhu and Zhuang. We then assume that C has enough projectives and injectives, and prove that C is locally finite if and only if its projective and injective subcategories are locally finite, the Euler functions associated with Auslander-Reiten relations have finite support, stable and costable morphisms detect ordinary morphisms away from the projective and injective boundary, and Rel(C) = AR(C). Our results recover the classical module and triangulated cases. They also explain why the two one-sided support conditions are equivalent in the triangulated setting, but may differ in a general extriangulated category.
