Relative cluster categories and Higgs categories with infinite-dimensional morphism spaces

发布时间：2023-09-11 来源：赢咖3 浏览次数：

Speaker:	吴燚林	DateTime:	2023年9月17日（周日）上午9:00-10：00
Brief Introduction to Speaker: 吴燚林博士于2022年毕业于巴黎西岱大学（原巴黎七大）、华东师范大学，现为中国科学技术大学博士后。现阶段主要从事丛代数范畴化的研究。		Place:	6号楼2楼报告厅
Abstract:Cluster categories were introduced in 2006 by Buan–Marsh–Reineke–Reiten–Todorov in order to categorify acyclic cluster algebras without coefficients. Their construction was generalized by Amiot to Jacobi-finite quivers with potential (2009). Later, Plamondon generalized it to arbitrary cluster algebras associated with quivers (2009 and 2011). Cluster algebras with coefficients are important since they appear in nature as coordinate algebras of varieties like Grassmannians, double Bruhat cells, unipotent cells, ....The work of Geiss-Leclerc-Schröer often yields Frobenius exact categories which allow to categorify such cluster algebras. In previous work, we have constructed Higgs categories and relative cluster categories in the relative Jacobi-finite setting (arXiv:2109.03707). Higgs categories generalize the Frobenius categories used by Geiss-Leclerc-Schröer. In this talk, we give the construction of the Higgs category and of the relative cluster category in the relative Jacobi...