论文标题
仿射非共同的几何形状
Affine noncommutative geometry
论文作者
论文摘要
从仿射角度来看，这是对非交流几何形状的介绍，即使用坐标。空格$ \ MATHBB r^n，\ MATHBB C^n $在操作式代数中没有免费类似物，但是相应的单元Spheres $ s^{n-1} _ \ Mathbb r，s^{n-1} _ \ Mathbb c $ Do具有免费的类似模拟$ s^n-1} _ \ bb r，+}，s^{n-1} _ {\ mathbb c，+} $。有许多实例的实例submanifolds $ x \ subset s^{n-1} _ {\ Mathbb r，+}，s^{n-1} _ {\ m athbb c，+} $，其中一些是riemannian的风味，带有riemannian的风味，带有haar intemitation a haar intemation $ \ int $ \ int y lig \ int lim \ int：c（c）c（x）c（x）c（x）c（x）我们将主要关注免费的几何形状，但是我们将讨论一些相关的几何形状，称为Easy，完成由4个主要几何形状形成的图片，即真实/复杂，经典/免费。
This is an introduction to noncommutative geometry, from an affine viewpoint, that is, by using coordinates. The spaces $\mathbb R^N,\mathbb C^N$ have no free analogues in the operator algebra sense, but the corresponding unit spheres $S^{N-1}_\mathbb R,S^{N-1}_\mathbb C$ do have free analogues $S^{N-1}_{\mathbb R,+},S^{N-1}_{\mathbb C,+}$. There are many examples of real algebraic submanifolds $X\subset S^{N-1}_{\mathbb R,+},S^{N-1}_{\mathbb C,+}$, some of which are of Riemannian flavor, coming with a Haar integration functional $\int:C(X)\to\mathbb C$, that we will study here. We will mostly focus on free geometry, but we will discuss as well some related geometries, called easy, completing the picture formed by the 4 main geometries, namely real/complex, classical/free.
