报告人：高楠教授 （上海大学）

报告时间：2023年4月26日 下午 14：30-15：30

腾讯会议：483 852 416

题目：Indecomposables in monomorphism categories

摘要：

We investigate the (separated) monomorphism category mono(Q,A) of a quiver over a Artin algebra . We show that there exists a representation equivalence in the sense of Auslander from \overline{mono}(Q,A) to rep(Q,\overline{mod}A), where modA is the category of finitely generated modules and \overline{mod}A and \overline{mono}(Q,A) denote the respective injectively stable categories. Furthermore, if Q has at least one arrow, then we show that this is an equivalence if and only if A is hereditary.  In general, the representation equivalence induces a bijection between indecomposable objects in rep(Q,\overline{mod}A) and non-injective indecomposable objects in mono(Q,A), and we show that the generalized Mimo-construction, an explicit minimal right approximation into mono(Q,A), gives an inverse to this bijection.  We apply these results to describe the indecomposables in the monomorphism category of a radical-square-zero Nakayama algebra, and to give a bijection between the indecomposables in the monomorphism category of two artinian uniserial rings of Loewy length 3 with the same residue field.

报告人简介： 高楠，上海大学教授、博士生导师。兼任美国数学评论评论员，美国、德国等主办的多个国际数学期刊审稿人。主要从事代数表示论、三角范畴、导出范畴、Gorenstein同调代数等研究。在Comm.Contem.Math.、J.Algebra等SCI收录期刊发表学术论文30余篇; 多次受邀在“世界华人数学家大会”“中日韩环论国际会议大会报告”“中国数学会年会”“全国代数学学术会议”等国内外重要学术会议上作报告；参与国家级一流本科课程1门、上海市级精品课程2门；参获上海市自然科学奖3等奖1项、上海市级教学成果奖1等奖1项。