非交换刚性
Noncommutative Rigidity
摘要：
使用非常弱的标准，什么可能构成一个非交换几何，我表明，一个伪黎曼流形只能顺利变形为非交换几何，如果某些几何障碍消失。这些障碍可以表示为一个偏微分方程组系统的度量和泊松结构，描述的非交换性。我通过计算非交换几何和量子群的著名例子的障碍来说明这一点。这些严格的条件可能会使人对非对易变形时空的概念产生怀疑。
英文摘要：
Using very weak criteria for what may constitute a noncommutative geometry, I show that a pseudo-Riemannian manifold can only be smoothly deformed into noncommutative geometries if certain geometric obstructions vanish. These obstructions can be expressed as a system of partial differential equations relating the metric and the Poisson structure that describes the noncommutativity. I illustrate this by computing the obstructions for well known examples of noncommutative geometries and quantum groups. These rigid conditions may cast doubt on the idea of noncommutatively deformed space-time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
