Homological structures at the interface of abstract representation theory and algebraic Lie theory

抽象表示论与代数李理论接口处的同调结构

• 批准号: 125747198
• 负责人: Professor Dr. Steffen Koenig
• 金额: --
• 依托单位: Institut für Algebra und Zahlentheorie (IAZ)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/125747198?language=en
• 关键词: Homological; structures; interface; abstract; representation

This project will investigate homological structures of algebras at the interface of abstract representation theory of finite dimensional algebras and algebraic Lie theory. The main topics will be (a) homological dimensions such as representation dimension, dominant dimension and finitistic dimension, (b) homological conjectures such as finitistic dimension conjecture, Nakayama’s conjecture, Cartan determinant conjecture and strong no loops conjecture, (c) structures of algebras such as finite dimensional and affine cellular and quasi-hereditary structures and Borel subalgebras and bocses, (d) equivalences of abelian and triangulated categories, tilting objects and recollements. Particular attention will be paid to connections and interactions between these topics. The results will be tested on and applied to algebras of interest in algebraic Lie theory such as Schur algebras of classical groups, blocks of the Bernstein-Gelfand-Gelfand category O, Brauer algebras, group algebras of symmetric groups and affine Hecke algebras.

本计画将探讨有限维代数的抽象表示理论与代数李理论的介面上代数的同调结构。主要内容有：（a）同调维数，如表示维数、支配维数和有限维数;（B）同调代数，如有限维数猜想、Nakayama猜想、Cartan行列式猜想和强无环猜想;（c）代数结构，如有限维、仿射胞腔结构、拟遗传结构和Borel子代数和bocses;（d）阿贝尔范畴和三角范畴的等价性、倾斜物体和倾斜元素。将特别注意这些主题之间的联系和相互作用。这些结果将被测试和应用于代数李理论中感兴趣的代数，如经典群的Schur代数，Bernstein-Gelfand-Gelfand O类的块，Brauer代数，对称群的群代数和仿射Hecke代数。