Noncommutative global Kosul duality and homotopy theory

非交换全局 Kosul 对偶性和同伦理论

• 批准号: 2601010
• 金额: --
• 依托单位: Lancaster University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2601010
• 关键词: Noncommutative; global; Kosul; duality; homotopy

Global Koszul duality and applications.Differential graded Koszul duality is a far-reaching phenomenon linking the behaviour of algebras and conilpotent coalgebras, seemingly very different objects. It has been much studied in connection with rational homotopy theory and deformation theory. Recently it has been observed that a more general form of Koszul duality than previously observed, can be constructed; it involves general, as opposed to conilpotent, coalgebras. This project will explore topological ramifications of this global Koszul duality.

整体Koszul对偶及其应用微分分次Koszul对偶是一个影响深远的现象，它联系了代数和幂次余代数的行为，这两个对象看起来非常不同。它与有理同伦理论和变形理论有着密切的联系。最近人们发现，可以构造一种比以前观察到的更一般的Koszul对偶形式;它涉及一般的余代数，而不是幂次余代数。这个项目将探索这个全球Koszul对偶的拓扑分支。