Quasifolds, diffeology and noncommutative geometry

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2020-05-19 DOI:10.4171/JNCG/419

Patrick Iglesias-Zemmour, E. Prato

引用次数: 8

Abstract

After embedding the objects quasifolds into the category {Diffeology}, we associate a C*-agebra with every atlas of any quasifold, and show how different atlases give Morita equivalent algebras. This builds a new bridge between diffeology and noncommutative geometry (beginning with the today classical example of the irrational torus) which associates a Morita class of C*-algebras with a diffeomorphic class of quasifolds.

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准折叠，微分学和非交换几何

在将对象拟折叠嵌入到范畴{Diffology}中后，我们将C*-代数与任何拟折叠的每个图谱相关联，并展示了不同的图谱如何给出Morita等价代数。这在微分学和非对易几何之间建立了一座新的桥梁（从今天无理环面的经典例子开始），它将C*-代数的Morita类与拟折叠的微分同胚类联系起来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.