报告题目：Rigidity dimension of algebras

报告人：陈红星

时间：2021年12月17日上午10：00

摘要：Rigidity dimension of algebras is a new homological dimension which measures the quality of resolutions of algebras by algebras of finite global dimension and large dominant dimension. It is related to quasi-hereditary covers, Schur-Weyl duality, non-commutative crepant resolutions, Hochschild cohomology and so on. A basic problem on rigidity dimension is how to calculate this dimension for a given algebra. In this talk, we shall introduce some elementary methods to calculate rigidity dimensions of algebras. As an application, we show that the rigidity dimensions of the trivial extension algebras of hereditary algebras of Dynkin type A_n and D_n (n>3) are 2n and 5, respectively. Coincidently, for A_n and D_4, the rigidity dimension is reached by the dominant dimension of higher Auslander algebra. This talk is based on some joint work with Ming Fang, Otto Kerner, Steffen Koenig and Kunio Yamagata, and also with Wei Xing (Uppsala University).

报告人简介：

陈红星，首都师范大学副教授。博士毕业于北京师范大学，2011-2013年在北京大学国际数学研究中心做博士后。2021获国家自然科学基金优秀青年科学基金。曾获教育部学术新人奖，入选北京市科技新星计划。曾主持国家自然科学基金面上、青年项目、北京市自然科学基金青年项目、中国博士后科学基金，并参与国家自然科学基金重点项目和北京市教育委员会科技计划重点项目。 主要从事代数表示论和同调代数的研究，在同调猜想、导出范畴、无限维倾斜理论、代数K-理论等方面取得了一系列的研究成果，彻底解决了关于导出模范畴Jordan-Holder定理存在性问题。 研究成果发表在Proc. Lond. Math. Soc., Int Math Res Notices, Forum Math, J. London. Math. Soc.等国际知名数学杂志。