报告题目：n-translation algebras and higher representation theory

报告人：郭晋云 湖南师范大学 教授 博士生导师

报告摘要：Start with a stable $n$-translation algebra, we study the $\tau$-slice algebra and dual $\tau$-slice algebras. Such algebras, especially dual $\tau$-slice algebras, are closed related to Iyama's higher representation theory. We show that $n$-APR tilts of such algebra are characterized by $\tau$-mutation, the Auslander of $\tau_n$ closure and $\nu_n$-closure are characterised by the $\mathbb Z|n Q$ construction introduced for constructing $n$-translation algebras. In the Koszul case, such dual $\tau$-slice algebras are $(n-1)$-Fano algebras introduced by Minamoto. Using $n$-translation algebra, we give a construction of a sequence of $n+t$-Fano algbras when an $n$-Fano algebra is given. We also show that for such  $(n-1)$-Fano algebra, preprojective algebras and the twisted trivial extension of its quadratic dual are related by quadratic dual.

报告时间： 2018年4月20日上午8:00-8:45

报告地点：002cc白菜资讯三楼专家接待室

报告人简介：郭晋云：湖南师范大学数学与统计学院教授，博士生导师。从事代数表示论及相关领域研究、主要研究兴趣为高维表示理论、McKay箭图相关问题及非交换代数几何。北京师范大学数学系博士，德国比勒费尔德大学数学系洪堡基金博士后，曾任墨西哥国立自治大学数学研究所研究员，湖南师范大学学术委员会副主任、理学院经理。享受国务院特殊津贴，十余次主持国家自然科学基金，在《J.of Algebra》、《Sci.China》等刊物发表论文50余篇。