On homological dimensions and combinatorics of finite dimensional algebras

关于有限维代数的同调维数和组合数学

• 批准号: 428999796
• 负责人: Dr. Rene Marczinzik
• 金额: --
• 依托单位: Mathematisches Institut (MI)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/428999796?language=en
• 关键词: homological; dimensions; combinatorics; finite; dimensional

We aim to find new connections between the homological algebra of incidence algebras of posets and their combinatorial properties. We also want to extend the theory of cluster tilting objects and higher Auslander algebras of Iyama and apply them to Cohen-Macaulay Artin algebras in the sense of Auslander and Reiten. Moreover, we want to study homological properties of the Jacobson radical and its higher syzygies that have a connection to the finitistic dimension conjecture.

我们的目的是找到偏序集关联代数的同调代数与它们的组合性质之间的新的联系。我们还想把Iyama的簇倾斜体理论和高阶Auslander代数推广到Auslander和Reiten意义下的Cohen-Macaulay Artin代数。此外，我们还想研究与有限维猜想有关的Jacobson根及其高次合群的同调性质。