Actions of 2-groupoids on C*-algebras

2-群形对 C*-代数的作用

• 批准号: 128675010
• 负责人: Professor Dr. Ralf Meyer
• 金额: --
• 依托单位: Mathematisches Institut (MI)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/128675010?language=en
• 关键词: Actions; groupoids; algebras

Groupoids describe geometric spaces with singularities and are a central object of study in noncommutative geometry. Several problems in geometry and mathematical physics lead to singularities for which groupoids are inadequate; a typical example are foliations with non-Hausdorff holonomy groupoid. But these situations may be described in the framework of higher category theory using 2-groupoids. The goals of this project are to attach C*-algebras to such 2-groupoids; to study their actions on C*-algebras and crossed products for such actions, and the K-theory of the resulting C*-algebras. The natural notion of action for 2-groupoids is more flexible than the usual one and includes Green’s twisted group actions as a special case. Furthermore, it allows for proper actions on C*-algebras of holonomy 2-groupoids of foliations even if the holonomy groupoid is non-Hausdorff.

群胚描述了具有奇点的几何空间，是非交换几何的中心研究对象。几何和数学物理中的几个问题会导致群胚不适用的奇点，一个典型的例子是具有非豪斯多夫完整群胚的叶理。但这些情况可以在高级范畴理论的框架下用2-群胚来描述。这个项目的目标是将C*-代数附加到这样的2-广群上;研究它们在C*-代数上的作用和这种作用的交叉积，以及由此产生的C*-代数的K-理论。2-群胚作用的自然概念比通常的概念更灵活，并且包括绿色的扭曲群作用作为特例。此外，它允许在叶子的完整2-广群的C*-代数上的适当作用，即使完整广群是非Hausdorff的。

项目成果

Non-Hausdorff symmetries of C*-algebras

C* 代数的非豪斯多夫对称性

• DOI: 10.1007/s00208-010-0630-3
• 发表时间: 2012
• 期刊: Mathematische Annalen
• 影响因子: 1.4
• 作者: Alcides Buss;Ralf Meyer;Chenchang Zhu
• 通讯作者: Chenchang Zhu

A higher category approach to twisted actions on c* -algebras

c* 代数扭曲作用的更高类别方法

• DOI: 10.1017/s0013091512000259
• 发表时间: 2013
• 期刊: Proceedings of the Edinburgh Mathematical Society
• 影响因子: 0.7
• 作者: Alcides Buss;Ralf Meyer;Chenchang Zhu
• 通讯作者: Chenchang Zhu

Strictification of étale stacky Lie groups

étale 堆叠李群的严格化

• DOI: 10.1112/s0010437x11007020
• 发表时间: 2012
• 期刊: Compositio Mathematica
• 影响因子: 1.8
• 作者: Giorgio Trentinaglia;Chenchang Zhu
• 通讯作者: Chenchang Zhu