Standard objects, filtered categories and representations of boxes

标准对象、过滤类别和框表示

• 批准号: 282852568
• 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: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/282852568?language=en
• 关键词: Standard; objects; filtered; categories; representations

There are many examples of standard objects: Verma modules of Lie algebras, Weyl modules of algebraic groups, exceptional coherent sheaves, ... The category of objects with standard filtration is used in the context of Ringel duality and of standardisation and for constructing Morita or derived equivalences with modules over quasi-hereditary algebras. In joint work with Julian Külshammer and Sergiy Ovsienko, it has been shown that this category is equivalent to the category of representations of a box. As an application, the problem of existence of exact Borel subalgebras of quasi-hereditary algebras (up to Morita equivalence) could be solved positively and thus an analogue of the theorem of Poincare, Birkhoff and Witt could be established.This project aims at developing and extending this approach and using it for investigating Ringel duality and tilting modules as well as for determining representation types and for computing representations and cohomology.

有许多标准对象的例子：李代数的Verma模，代数群的Weyl模，例外凝聚层，…具有标准滤子的对象范畴被用在Ringel对偶和标准化的上下文中，并用于构造拟遗传代数上的Morita等价或与模的导出等价。在与Julian Külshammer和Sergiy Ovsienko的共同工作中，证明了这个范畴等价于盒的表示范畴。作为一个应用，拟遗传代数(直到Morita等价)的精确Borel子代数的存在性问题可以被正解，从而可以建立一个类似于Poincare，Birkhoff和Witt的定理.本项目旨在发展和推广这一方法，并将其用于研究Ringel对偶和倾斜模，以及确定表示类型，计算表示和上同调.

项目成果

Higher Nakayama algebras I: Construction

• DOI: 10.1016/j.aim.2019.05.026
• 发表时间: 2016-04
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Gustavo Jasso;Julian Kulshammer

Representations of algebras

• DOI: 10.1090/conm/705
• 发表时间: 2017-06
• 期刊: A Tour of Representation Theory
• 作者: Ryan Kinser

Ringel duality as an instance of Koszul duality

林格尔对偶性作为科祖尔对偶性的一个实例

• DOI: 10.1016/j.jalgebra.2018.03.025
• 发表时间: 2018
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: Agnieszka Bodzenta;Julian Külshammer
• 通讯作者: Julian Külshammer