Hopf cyclic cohomology, twisted local index formula, and noncommutative complex geometry

Hopf 循环上同调、扭曲局部指数公式和非交换复几何

• 批准号: 184060-2009
• 负责人: Khalkhali, Masoud
• 金额: $ 2.04万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=523031
• 关键词: Hopf; cyclic; cohomology; twisted; local

This proposal consists of several rather independent components: the local index formula for twisted spectral triples; an elaborate study of Hopf cyclic cohomology; and noncommutative complex geometry. The notion of a twisted spectral triple has recently been introduced by Connes and Moscovici. It aims to extend the index theory to a type III setting. Here by type III we mean a situation (as in type III von Neumann algebras) where the underlying noncommutative space admits no non-zero traces. The twist automorphism is

这个建议由几个相当独立的组件：扭曲的频谱三元组的本地指数公式;一个精心研究的霍普夫循环上同调;和非交换复杂的几何。 扭曲谱三元组的概念最近由Connes和Moscovici提出。它旨在将指数理论扩展到第三类环境。这里的III型是指一种情况（如在III型冯诺依曼代数中），其中底层的非交换空间不允许非零迹。扭曲自同构是