Cyclic A-infinity algebras and their Koszul duals

循环 A-无穷代数及其 Koszul 对偶

• 批准号: 1801259
• 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: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1801259
• 关键词: Cyclic; infinity; algebras; their; Koszul

The notion of a cyclic A-infinity algebra appears naturally in many contexts of algebra and topology, e.g. as cochain algebras of Poincare duality spaces. It is important to characterize intrinsically their Koszul duals. Such a characterization was provided in a recent work of Van den Berg but inly under rather restrictive grading assumptions that are, in particular, exclude the example mentioned above. The goal of this project is to remove these assumptions and also refine the characterization to the commutative case. A corollary would be an intrinsic characterization of homotopy Lie algebras of Poincare duality spaces.

循环A-无穷代数的概念自然出现在代数和拓扑学的许多上下文中，例如庞加莱对偶空间的上链代数。重要的是要从本质上描述他们的Koszul。这种表征是在货车登贝格的最近的工作，但在相当严格的分级假设，特别是排除上述例子。这个项目的目标是删除这些假设，并完善的特征，交换的情况下。一个推论是Poincare对偶空间的同伦李代数的一个内在特征。